Let (A, ) be a partial order with two minimal elements a, b and a maximum element c. Let P:A > {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) P(b) for all satisfying a b, where stands for logical implication. Which of the following statements cannot be true?

P(x) = True for all x S such that x b

P(x) = False for all x S such that b x and x c

P(x) = False for all x S such that x a and x c

P(x) = False for all x S such that a x and b x

Consider the ordering relation a | b N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________

Every subset of N has an upper bound under |

(N,|) is a lattice but not a complete lattice

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) P. ii)(a, b) P if and only if a % 10 b % 10 and (a/10, b/10) P. Consider the following ordered pairs:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)

nThe ordered pairs of natural numbers are contained in P are ______ and ______

The less-than relation, <, on a set of real numbers is ______

a partial ordering since it is asymmetric and reflexive

not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric

a partial ordering since it is asymmetric and reflexive

a partial ordering since it is antisymmetric and reflexive

not a partial ordering because it is not antisymmetric and reflexive

Explore topic-wise MCQs in Discrete Mathematics.

This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.	Let (A, ) be a partial order with two minimal elements a, b and a maximum element c. Let P:A > {True, False} be a predicate defined on A. Suppose that P(a) = True, P(b) = False and P(a) P(b) for all satisfying a b, where stands for logical implication. Which of the following statements cannot be true?
A.	P(x) = True for all x S such that x b
B.	P(x) = False for all x S such that b x and x c
C.	P(x) = False for all x S such that x a and x c
D.	P(x) = False for all x S such that a x and b x
Answer» E.

Discussion

2.	A partial order is defined on the set S = {x, b₁, b₂, b_n, y} as x b_i for all i and b_i y for all i, where n 1. The number of total orders on the set S which contain the partial order is ______
A.	n+4
B.	n<sup>2</sup>
C.	n!
D.	3
Answer» D. 3

Discussion

3.	Consider the ordering relation a \| b N x N over natural numbers N such that a \| b if there exists c belong to N such that a*c=b. Then ___________
A.	\| is an equivalence relation
B.	It is a total order
C.	Every subset of N has an upper bound under \|
D.	(N,\|) is a lattice but not a complete lattice
Answer» E.

Discussion

4.	A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) P. ii)(a, b) P if and only if a % 10 b % 10 and (a/10, b/10) P. Consider the following ordered pairs: i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)
A.	nThe ordered pairs of natural numbers are contained in P are ______ and ______
B.	(145, 265) and (0, 153)
C.	(22, 101) and (0, 153)
D.	(101, 22) and (145, 265)
E.	(101, 22) and (0, 153)
Answer» E. (101, 22) and (0, 153)

Discussion

5.	Suppose X = {a, b, c, d} and ₁ is the partition of X, ₁ = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________
A.	15
B.	10
C.	34
D.	5
Answer» C. 34

Discussion

6.	The less-than relation, <, on a set of real numbers is ______
A.	not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric
B.	a partial ordering since it is asymmetric and reflexive
C.	a partial ordering since it is antisymmetric and reflexive
D.	not a partial ordering because it is not antisymmetric and reflexive
Answer» B. a partial ordering since it is asymmetric and reflexive

Discussion

7.	Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______
A.	6
B.	5
C.	9
D.	4
Answer» C. 9

Discussion

Explore topic-wise MCQs in Discrete Mathematics.

A partial order is defined on the set S = {x, b1, b2, bn, y} as x bi for all i and bi y for all i, where n 1. The number of total orders on the set S which contain the partial order is ______

Consider the ordering relation a | b N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) P. ii)(a, b) P if and only if a % 10 b % 10 and (a/10, b/10) P. Consider the following ordered pairs:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)

Suppose X = {a, b, c, d} and 1 is the partition of X, 1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________

The less-than relation, <, on a set of real numbers is ______

Let a set S = {2, 4, 8, 16, 32} and <= be the partial order defined by S <= R if a divides b. Number of edges in the Hasse diagram of is ______

A partial order is defined on the set S = {x, b₁, b₂, b_n, y} as x b_i for all i and b_i y for all i, where n 1. The number of total orders on the set S which contain the partial order is ______

A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) P. ii)(a, b) P if and only if a % 10 b % 10 and (a/10, b/10) P. Consider the following ordered pairs:
i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)

Suppose X = {a, b, c, d} and ₁ is the partition of X, ₁ = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________