A binary operation ⊕ on a set of integers is defined as x⊕ y = x2 + y2. Which one of the following statements is TRUE about ⊕?

Both commutative and associative

Commutative but not associative

Both commutative and associative

Associative but not commutative

Neither commutative nor associative

Let x be a non-optimal feasible solution of a linear programming maximization problem and y a dual feasible solution, then

the primal objective value of x is greater than the dual objective value at y

the primal objective value at x can be equal to the dual objective value at y

the primal objective value at x is less than the dual objective value at y

Consider two subsets of ℝ2 given as, S1 = {[1, -2], [3, 5]} and S2 = {[1, 1], [0, 0]}. Then,

S1 is not a basis for ℝ2 but S2 is a basis for ℝ2.

neither S1 nor S2 are bases for ℝ2.

S1 is a basis for ℝ2 but S2 is not a basis for ℝ2.

If g(x) = 1 – x and $h\left( x \right) = \frac{x}{{x - 1}},\;then\frac{{g\left( {h\left( x \right)} \right)}}{{h\left( {g\left( x \right)} \right)}}\;is:$

$\frac{{h\left( x \right)}}{{g\left( x \right)}}$

$\frac{{g\left( x \right)}}{{h\left( x \right)}}$

$\frac{x}{{{{\left( {1 - x} \right)}^2}}}$

Let G be a group order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

Both G and H are always cyclic.

G is always cyclic, but H may not be cyclic.

G may not be cyclic, but H is always cyclic.

Both G and H are always cyclic.

Both G and H may not be cyclic.

Consider two subsets of R3 given asS1 = {[1, -1, 2], [3, 2, -1]} and S2 = {[2, 7, -3],[-6, -21, 9]}. Then:

S1 cannot be enlarged but S2 can be enlarged to a basis for R3

neither S1 and S2 can be enlarged to a basis for R3

S1 can be enlarged but S2 cannot be enlarged to a basis for R3

S1 cannot be enlarged but S2 can be enlarged to a basis for R3

both S1 and S2 can be enlarged to a basis for R3

Consider the operationsf (X, Y, Z) = X’ YZ + XY’ + Y’Z’ and g (X, Y, Z) = X’ YZ + X’ YZ’ + XYWhich of the following is correct?

Only $g$ is functionally complete

Both $f$ and $g$ are functionally complete

Only $f$ is functionally complete

Only $g$ is functionally complete

Neither $f$ nor $g$ is functionally complete

Let X and Y be finite sets and f: X → Y be a function. Which one of the following statements in TRUE?

For any subsets A and B of X, |f (A ∪ B)| = |f(A)| + |F(B)|

For any subsets A and B of X, f(A ∩ B) = f(A) ∩ f(B)

For any subsets A and B of X, |g(A ∩ B)| = min{|f(A)|, |f(B)|}

For any subset S and T of Y, F-1(S∪ T) = f-1(S)∩ f-1(T)

Let f be a mapping from X = {1, 2, 3, ....., 50} to itself such that for m, n ϵ X, m ≤ n implies that f(m) ≤ f(n). Then which of the following is true?

For every m ϵ X, we may have f(m) = m - 1

There is m ϵ X such that f(m) = m

For every m ϵ X, we may have f(m) = m - 1

For every m ϵ X, we may have f(m) = m + 1

For every even m ϵ X, we must have f(m) = 1/2 m

A function f(x) is defined in the following way:f(x) = -x, x ≤ 0= x, 0 < x < 1= 2 - x, x ≥ 1In this case, the function f(x) is:

continuous at x = 0 and discontinuous at x = 1

continuous at both x = 0 and x = 1

continuous at x = 0 and discontinuous at x = 1

discontinuous at x = 0 and continuous at x = 1

discontinuous at both x = 0 and x = 1

(G, *) is an abelian group. then

x = x-1 for any x belonging to G

x = x2 for any x belonging to G

(x * y)2 = x2 * y2, for any x, y belonging to G

A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

if a relation S is circular and symmetric, then S is an equivalence relation.

If a relation S is transitive and circular, then S is an equivalence relation.

If a relation S is reflexive and symmetric, then S is an equivalence relation.

if a relation S is reflexive and circular, then S is an equivalence relation.

if a relation S is circular and symmetric, then S is an equivalence relation.

Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively.Which one of the following is NOT CORRECT?

$\overline{{(P⊕Q)}} =P⊙Q$

$(P⊕\bar P)⊕Q=(P⊙\bar P)⊙\bar Q$

Consider the set of integers I. Let D denote “divides with an integer quotient” (e.g. $4D8$ but$4 \not D 7$). Then D is

Reflexive, not symmetric, transitive

Not reflexive, not antisymmetric, transitive

Reflexive, antisymmetric, transitive

Not reflexive, not antisymmetric, not transitive

Let R be the relation on the set of positive integers such that aRb if and only if 'a 'and 'b' are distinct and have a common divisor other than 1. Which one of the following statements about 'R' is true?

𝑅 is symmetric and reflexive but not transitive

𝑅 is reflexive but not symmetric and not transitive

𝑅 is transitive but not reflexive and not symmetric

𝑅 is symmetric but not reflexive and not transitive

Name the functions of the graphs a, b, c, d

a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2

$ a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left| x \right|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x + 2$

a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2

$a\;:f\left( x \right) = - x;\;b\;:f\left( x \right) = \left| x \right|;\;c\;:f\left( x \right) = - {e^x};\;d\;:f\left( x \right) = x + 2$

$a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left| {{x^2}} \right|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x - 2$

Consider the following sets, where n > 2:S1: Set of all n x n matrices with entries from the set {a, 6, c}S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0,1,2}Which of the following choice(s) is/are correct?

There exists a surjection from S1 to S2.

There does not exist an injection from S1 to S2.

There exists a bijection from S1 to S2

There exists a surjection from S1 to S2.

There does not exist a bijection from S1 to S2

Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p – s = q – r. Which one of the following is true about R?

Neither reflexive nor symmetric

A subset H of a group (G, ∗) is a group if

H contains the identity element

49 + Mcqs in Set Theory & Algebra in Engineering Mathematics Page 1 McqOptions

1.	Let Booleam operation * is defined as a * b = a + b̅. If m = a * b, then the value of m * b is:
A.	a
B.	m
C.	1
D.	a̅ + b
Answer» C. 1

Discussion

2.	A binary operation ⊕ on a set of integers is defined as x⊕ y = x2 + y2. Which one of the following statements is TRUE about ⊕?
A.	Commutative but not associative
B.	Both commutative and associative
C.	Associative but not commutative
D.	Neither commutative nor associative
Answer» B. Both commutative and associative

Discussion

3.	Let x be a non-optimal feasible solution of a linear programming maximization problem and y a dual feasible solution, then
A.	the primal objective value of x is greater than the dual objective value at y
B.	the primal objective value at x can be equal to the dual objective value at y
C.	the primal objective value at x is less than the dual objective value at y
D.	the dual can be unbounded
Answer» D. the dual can be unbounded

Discussion

4.	Consider two subsets of ℝ2 given as, S1 = {[1, -2], [3, 5]} and S2 = {[1, 1], [0, 0]}. Then,
A.	S1 is not a basis for ℝ2 but S2 is a basis for ℝ2.
B.	neither S1 nor S2 are bases for ℝ2.
C.	both S1 and S2 are bases ℝ2.
D.	S1 is a basis for ℝ2 but S2 is not a basis for ℝ2.
Answer» E.

Discussion

5.	A cyclic permutation of length 2 is called
A.	coset
B.	Normal group
C.	Transposition
D.	kernel
Answer» D. kernel

Discussion

6.	Consider the Boolean operator # with the following properties:x # 0 = x, x # 1 = x̅, x # x = 0 and x # x̅ = 1. Then x # y is equivalent to
A.	xy̅ + x̅y
B.	xy̅ + x̅ y̅
C.	x̅y + xy
D.	xy + x̅ y̅
Answer» B. xy̅ + x̅ y̅

Discussion

7.	If g(x) = 1 – x and $h\left( x \right) = \frac{x}{{x - 1}},\;then\frac{{g\left( {h\left( x \right)} \right)}}{{h\left( {g\left( x \right)} \right)}}\;is:$
A.	$\frac{{h\left( x \right)}}{{g\left( x \right)}}$
B.	-1/x
C.	$\frac{{g\left( x \right)}}{{h\left( x \right)}}$
D.	$\frac{x}{{{{\left( {1 - x} \right)}^2}}}$
Answer» B. -1/x

Discussion

8.	Consider the group Z495 under addition modulo 495.(i) {0, 99, 198, 307, 406} is the unique subgroup of Z495 of order 5.(ii) {0, 55, 110, 165, 220, 275, 330, 385, 440} is the unique subgroup of Z495 of order 9.Then,
A.	(i) is true, but (ii) is false
B.	(ii) is true, but (i) is false
C.	both (i) and (ii) are true
D.	both (i) and (ii) are false
Answer» D. both (i) and (ii) are false

Discussion

9.	For a set A, the power set of A is denoted by 2A. If A = {5, {6}, {7}}, which of the following options are TRUE?I. Φ ϵ 2AII. Φ ⊆ 2AIII. {5, {6}} ∈ 2AIV. {5, {6}} ⊆ 2A
A.	I and III only
B.	II and III only
C.	I, II and III only
D.	I, II and IV only
Answer» D. I, II and IV only

Discussion

10.	If G is a group of even order, then an element a ≠ e, satisfying
A.	a2 = e
B.	a3 = e
C.	a5 = e
D.	a7 = e
Answer» B. a3 = e

Discussion

11.	Any group of order 3 is
A.	cyclic
B.	abelian
C.	infinite cyclic group
D.	none of these
Answer» B. abelian

Discussion

12.	Let G be a group order 6, and H be a subgroup of G such that 1 < \|H\| < 6. Which one of the following options is correct?
A.	G is always cyclic, but H may not be cyclic.
B.	G may not be cyclic, but H is always cyclic.
C.	Both G and H are always cyclic.
D.	Both G and H may not be cyclic.
Answer» C. Both G and H are always cyclic.

Discussion

13.	Consider two subsets of R3 given asS1 = {[1, -1, 2], [3, 2, -1]} and S2 = {[2, 7, -3],[-6, -21, 9]}. Then:
A.	neither S1 and S2 can be enlarged to a basis for R3
B.	S1 can be enlarged but S2 cannot be enlarged to a basis for R3
C.	S1 cannot be enlarged but S2 can be enlarged to a basis for R3
D.	both S1 and S2 can be enlarged to a basis for R3
Answer» C. S1 cannot be enlarged but S2 can be enlarged to a basis for R3

Discussion

14.	If the group (z, ∗) of all integers, where a ∗ b = a + b + 1 for all a, b ∈ z, the inverse of -2 is
A.	-2
B.	0
C.	-4
D.	2
Answer» C. -4

Discussion

15.	Consider the operationsf (X, Y, Z) = X’ YZ + XY’ + Y’Z’ and g (X, Y, Z) = X’ YZ + X’ YZ’ + XYWhich of the following is correct?
A.	Both $f$ and $g$ are functionally complete
B.	Only $f$ is functionally complete
C.	Only $g$ is functionally complete
D.	Neither $f$ nor $g$ is functionally complete
Answer» C. Only $g$ is functionally complete

Discussion

16.	Let X and Y be finite sets and f: X → Y be a function. Which one of the following statements in TRUE?
A.	For any subsets A and B of X, \|f (A ∪ B)\| = \|f(A)\| + \|F(B)\|
B.	For any subsets A and B of X, f(A ∩ B) = f(A) ∩ f(B)
C.	For any subsets A and B of X, \|g(A ∩ B)\| = min{\|f(A)\|, \|f(B)\|}
D.	For any subset S and T of Y, F-1(S∪ T) = f-1(S)∩ f-1(T)
Answer» E.

Discussion

17.	Let A be a finite set having x elements and let B be a finite set having y elements. What is the number of distinct functions mapping B into A.
A.	xy
B.	2(x + y)
C.	yx
D.	y! / (y - x)!
Answer» B. 2(x + y)

Discussion

18.	Let G be an arbitrary group. Consider the following relations on G:R1: ∀a, b ϵ G, a R1b if and only if ∃g ϵ G such that a = g-1bgR2: ∀a, b ϵ G, a R1b if and only if a = b-1Which of the above is/are equivalence relation/relations?
A.	R1 and R2
B.	R1 only
C.	R2 only
D.	Neither R1 nor R2
Answer» C. R2 only

Discussion

19.	Consider the Boolean function f = (a + bc)⋅(pq + r). Complement f' of function f is:
A.	(a' + b'c') ⋅ (p'q' + r')
B.	a'(b' + c') + (p' + q')r'
C.	(a' + b'c') + (p'q' + r')
D.	(a'b'c') + (p'q'r')
Answer» C. (a' + b'c') + (p'q' + r')

Discussion

20.	A binary relation R on N × N is defined as follows: (a, b)R(c, d) if a ≤ c or b ≤ d. Consider the following propositions:P: R is reflexiveQ: R is transitiveWhich one of the following statements is TRUE?
A.	Both P and Q are true.
B.	P is true and Q is false.
C.	P is false and Q is true.
D.	Both P and Q are false.
Answer» C. P is false and Q is true.

Discussion

21.	Logic gates required to built up a half adder circuit are,
A.	Ex – OR gate and NOR gate
B.	Ex – OR gate and OR gate
C.	Ex – OR gate and AND gate
D.	Ex – NOR gate and NAND gate
Answer» D. Ex – NOR gate and NAND gate

Discussion

22.	Let f be a mapping from X = {1, 2, 3, ....., 50} to itself such that for m, n ϵ X, m ≤ n implies that f(m) ≤ f(n). Then which of the following is true?
A.	There is m ϵ X such that f(m) = m
B.	For every m ϵ X, we may have f(m) = m - 1
C.	For every m ϵ X, we may have f(m) = m + 1
D.	For every even m ϵ X, we must have f(m) = 1/2 m
Answer» B. For every m ϵ X, we may have f(m) = m - 1

Discussion

23.	A function f(x) is defined in the following way:f(x) = -x, x ≤ 0= x, 0 < x < 1= 2 - x, x ≥ 1In this case, the function f(x) is:
A.	continuous at both x = 0 and x = 1
B.	continuous at x = 0 and discontinuous at x = 1
C.	discontinuous at x = 0 and continuous at x = 1
D.	discontinuous at both x = 0 and x = 1
Answer» B. continuous at x = 0 and discontinuous at x = 1

Discussion

24.	Boolean expression y.z + z is equal to which of the following?
A.	y + y.z
B.	y + z
C.	z
D.	y.z
Answer» D. y.z

Discussion

25.	At point x = 0, the function f(x) = \|x\| has
A.	Neither minimum nor maximum
B.	A maxima
C.	Point of inflecton
D.	A minima
Answer» E.

Discussion

26.	(G, *) is an abelian group. then
A.	x = x-1 for any x belonging to G
B.	x = x2 for any x belonging to G
C.	(x * y)2 = x2 * y2, for any x, y belonging to G
D.	G is of finite order
Answer» D. G is of finite order

Discussion

27.	If A = {x, y, z} and B = {u, v, w, x} and the universe is {s, t, u, v, w, x, y, z}Then (A ∪ B̅) ∩ (A ∩ B) is equal to
A.	{u, v, w, x}
B.	{x}
C.	{u, v, w, x, y z}
D.	{u, v, w}
Answer» C. {u, v, w, x, y z}

Discussion

28.	In C++, which of the following operator cannot be overloaded?
A.	^
B.	0
C.	. [dot]
D.	!
Answer» D. !

Discussion

29.	A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?
A.	If a relation S is transitive and circular, then S is an equivalence relation.
B.	If a relation S is reflexive and symmetric, then S is an equivalence relation.
C.	if a relation S is reflexive and circular, then S is an equivalence relation.
D.	if a relation S is circular and symmetric, then S is an equivalence relation.
Answer» D. if a relation S is circular and symmetric, then S is an equivalence relation.

Discussion

30.	A tautology is a Boolean formula that is always true. Which of the following is a tautology?
A.	x
B.	(x + x̅)y
C.	x + y̅ + x̅
D.	(xy) + x̅
Answer» D. (xy) + x̅

Discussion

31.	Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively.Which one of the following is NOT CORRECT?
A.	$\overline{{(P⊕Q)}} =P⊙Q$
B.	$\bar P⊕Q=P⊙Q$
C.	$\bar P ⊕\bar Q =P⊕Q$
D.	$(P⊕\bar P)⊕Q=(P⊙\bar P)⊙\bar Q$
Answer» E.

Discussion

32.	Consider the set of integers I. Let D denote “divides with an integer quotient” (e.g. $4D8$ but$4 \not D 7$). Then D is
A.	Reflexive, not symmetric, transitive
B.	Not reflexive, not antisymmetric, transitive
C.	Reflexive, antisymmetric, transitive
D.	Not reflexive, not antisymmetric, not transitive
Answer» E.

Discussion

33.	Let U = {1, 2, ..., n}. Let A = {(x, X)\|x ∈ X, X ⊆ U}. Consider the following two statementson \|A\|.I. \|A\| = n2n - 1II. $\left\| A \right\| = \mathop \sum \limits_{k = 1}^n k\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)$Which of the above statements is/are TRUE?
A.	Only I
B.	Only II
C.	Both I and II
D.	Neither I nor II
Answer» D. Neither I nor II

Discussion

34.	Consider the following relation on subsets of the set
A.	Both S1 and S2 are true
B.	S1 is true and S2 is false
C.	S2 is true and S1 is false
D.	Neither S1 nor S2 is true
Answer» B. S1 is true and S2 is false

Discussion

35.	Given the truth table of a Binary Operation $ as follows:XYX $ Y101111010001Identify the matching Boolean Expression.
A.	X $ ¬ Y
B.	¬ X $ Y
C.	¬ X $ ¬ Y
D.	none of the options
Answer» E.

Discussion

36.	Let R be the relation on the set of positive integers such that aRb if and only if 'a 'and 'b' are distinct and have a common divisor other than 1. Which one of the following statements about 'R' is true?
A.	𝑅 is symmetric and reflexive but not transitive
B.	𝑅 is reflexive but not symmetric and not transitive
C.	𝑅 is transitive but not reflexive and not symmetric
D.	𝑅 is symmetric but not reflexive and not transitive
Answer» E.

Discussion

37.	In any group, the number of improper subgroups is
A.	2
B.	3
C.	depends on the group
D.	1
Answer» B. 3

Discussion

38.	Let N be the set of natural numbers. Consider the following sets.P: Set of Rational numbers (positive and negative)Q: Set of functions from {0, 1} to NR: Set of functions from N to {0, 1}S: Set of finite subsets of N.Which of the sets above are countable?
A.	Q and S only
B.	P and S only
C.	P and R only
D.	P, Q and S only
Answer» E.

Discussion

39.	Name the functions of the graphs a, b, c, d
A.	$ a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left\| x \right\|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x + 2$
B.	a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2
C.	$a\;:f\left( x \right) = - x;\;b\;:f\left( x \right) = \left\| x \right\|;\;c\;:f\left( x \right) = - {e^x};\;d\;:f\left( x \right) = x + 2$
D.	$a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left\| {{x^2}} \right\|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x - 2$
Answer» B. a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2

Discussion

40.	If G is a cyclic group of order 24 and ${a^{2002}} = {a^n}$ where a ϵ G and 0 < n < 24. Then the value of n is
A.	4
B.	6
C.	8
D.	10
Answer» E.

Discussion

41.	A function λ, is defined by$\lambda \left( {p,\;q} \right) = \left\{ {\begin{array}{*{20}{c}} {{{\left( {p - q} \right)}^2},\;\;ir\;p \ge q,}\\ {p + q,\;\;if\;p < q.} \end{array}} \right.$The value of the expression $\frac{\lambda (-(-3+2),(-2+3))}{(-(-2+1))}$ is
A.	-1
B.	0
C.	16/3
D.	16
Answer» C. 16/3

Discussion

42.	Let f(x) = log \|x\| and g(x) = sin x. If A is the range of f(g (x)) and B is the range of g(f(x)) then A ∩ B
A.	[-1, 0]
B.	[-1, 0)
C.	[-∞, 0]
D.	[-∞, 1]
Answer» B. [-1, 0)

Discussion

43.	Consider the following sets, where n > 2:S1: Set of all n x n matrices with entries from the set {a, 6, c}S2: Set of all functions from the set {0,1, 2, ..., n2 — 1} to the set {0,1,2}Which of the following choice(s) is/are correct?
A.	There does not exist an injection from S1 to S2.
B.	There exists a bijection from S1 to S2
C.	There exists a surjection from S1 to S2.
D.	There does not exist a bijection from S1 to S2
Answer» C. There exists a surjection from S1 to S2.

Discussion

44.	Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p – s = q – r. Which one of the following is true about R?
A.	Both reflexive and symmetric
B.	Reflexive but not symmetric
C.	Not reflexive but symmetric
D.	Neither reflexive nor symmetric
Answer» D. Neither reflexive nor symmetric

Discussion

45.	Consider the following properties:A. ReflexiveB. AntisymmetricC. SymmetricLet A = {a, b, c, d, e, f, g} and R= {(a, a),(b, b),(c, d),(c, g),(d, g),(e, e),(f, f),(g, g)} be a relation on A. Which of the following property (properties) is (are) satisfied by the relation R ?
A.	Only A
B.	Only C
C.	Both A and B
D.	B and not A
Answer» E.

Discussion

46.	(p → q v r, q → s, r → s} is logically equivalent to
A.	q → r
B.	r → q
C.	p → s
D.	s → p
Answer» D. s → p

Discussion

47.	A subset H of a group (G, ∗) is a group if
A.	a, b ∈ H ⇒ a ∗ b ∈ H
B.	a ∈ H ⇒ a-1 ∈ H
C.	a, b ∈ H ⇒ a ∗ b-1 ∈ H
D.	H contains the identity element
Answer» B. a ∈ H ⇒ a-1 ∈ H

Discussion

48.	If R is commutative ring with unit element, M be an ideal of R and R/M is finite integral domain then
A.	M is a maximal ideal of R
B.	M is minimal ideal of R
C.	M is a vector space
D.	M is a coset of R
Answer» B. M is minimal ideal of R

Discussion

49.	Given:Statement A: All cyclic groups are an abelian group.Statement B: The order of the cyclic group is the same as the order of its generator.
A.	A and B are false
B.	A is true, B is false
C.	B is true, A is false
D.	A and B both are true
Answer» E.

Discussion

7.	If g(x) = 1 – x and \(h\left( x \right) = \frac{x}{{x - 1}},\;then\frac{{g\left( {h\left( x \right)} \right)}}{{h\left( {g\left( x \right)} \right)}}\;is:\)
A.	\(\frac{{h\left( x \right)}}{{g\left( x \right)}}\)
B.	-1/x
C.	\(\frac{{g\left( x \right)}}{{h\left( x \right)}}\)
D.	\(\frac{x}{{{{\left( {1 - x} \right)}^2}}}\)
Answer» B. -1/x

15.	Consider the operationsf (X, Y, Z) = X’ YZ + XY’ + Y’Z’ and g (X, Y, Z) = X’ YZ + X’ YZ’ + XYWhich of the following is correct?
A.	Both \(f\) and \(g\) are functionally complete
B.	Only \(f\) is functionally complete
C.	Only \(g\) is functionally complete
D.	Neither \(f\) nor \(g\) is functionally complete
Answer» C. Only \(g\) is functionally complete

31.	Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively.Which one of the following is NOT CORRECT?
A.	\(\overline{{(P⊕Q)}} =P⊙Q\)
B.	\(\bar P⊕Q=P⊙Q\)
C.	\(\bar P ⊕\bar Q =P⊕Q\)
D.	\((P⊕\bar P)⊕Q=(P⊙\bar P)⊙\bar Q\)
Answer» E.

39.	Name the functions of the graphs a, b, c, d
A.	\( a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left\| x \right\|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x + 2\)
B.	a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2
C.	\(a\;:f\left( x \right) = - x;\;b\;:f\left( x \right) = \left\| x \right\|;\;c\;:f\left( x \right) = - {e^x};\;d\;:f\left( x \right) = x + 2\)
D.	\(a\;:f\left( x \right) = x;\;b\;:f\left( x \right) = \left\| {{x^2}} \right\|;\;c\;:f\left( x \right) = {e^x};\;d\;:f\left( x \right) = x - 2\)
Answer» B. a : f(x) = x + 1; b : f(x) = x2; c : f(x) = log x; d : f(x) = x - 2

40.	If G is a cyclic group of order 24 and \({a^{2002}} = {a^n}\) where a ϵ G and 0 < n < 24. Then the value of n is
A.	4
B.	6
C.	8
D.	10
Answer» E.

41.	A function λ, is defined by\(\lambda \left( {p,\;q} \right) = \left\{ {\begin{array}{*{20}{c}} {{{\left( {p - q} \right)}^2},\;\;ir\;p \ge q,}\\ {p + q,\;\;if\;p < q.} \end{array}} \right.\)The value of the expression \(\frac{\lambda (-(-3+2),(-2+3))}{(-(-2+1))}\) is
A.	-1
B.	0
C.	16/3
D.	16
Answer» C. 16/3

Explore topic-wise MCQs in Engineering Mathematics.

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