Determine the characteristics of the relation aRb if a2 = b2.

Trichotomy, antisymmetry, and irreflexive

Symmetric, Reflexive, and transitive

Let R1 be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:i. An element a in A is related to an element b in B (under R1) if a * b is divisible by 3.

nii. An element a in B is related to an element b in C (under R2) if a * b is even but not divisible by 3. Which is the composite relation R1R2 from A to C?

R1R2 = {(1, 2), (1, 4), (3, 3), (5, 4), (5,6), (7, 3)}

R1R2 = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)}

R1R2 = {(2,2), (3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}

Consider the binary relation, A = {(a,b) | b = a 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?

{(a,b) | a > b and a, b belong to {1, 2, 3}}

{(a,b) | a >= b and a, b belong to {1, 2, 3}}

{(a,b) | a > b and a, b belong to {1, 2, 3}}

{(a,b) | a <= b and a, b belong to {1, 2, 3}}

{(a,b) | a = b and a, b belong to {1, 2, 3}}

Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?

number of subsets of the relation

Consider the relation: R (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R is _________

transitive and asymmetry relation

reflexive and antisymmetric relation

Explore topic-wise MCQs in Discrete Mathematics.

This section includes 6 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.	Determine the characteristics of the relation aRb if a² = b².
A.	Transitive and symmetric
B.	Reflexive and asymmetry
C.	Trichotomy, antisymmetry, and irreflexive
D.	Symmetric, Reflexive, and transitive
Answer» E.

Discussion

2.	Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below: i. An element a in A is related to an element b in B (under R₁) if a * b is divisible by 3.
A.	nii. An element a in B is related to an element b in C (under R<sub>2</sub>) if a * b is even but not divisible by 3. Which is the composite relation R<sub>1</sub>R<sub>2</sub> from A to C?
B.	R<sub>1</sub>R<sub>2</sub> = {(1, 2), (1, 4), (3, 3), (5, 4), (5,6), (7, 3)}
C.
D.	R<sub>1</sub>R<sub>2</sub> = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)}
E.	R<sub>1</sub>R<sub>2</sub> = {(2,2), (3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}
Answer» C.

Discussion

3.	Consider the binary relation, A = {(a,b) \| b = a 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?
A.	{(a,b) \| a >= b and a, b belong to {1, 2, 3}}
B.	{(a,b) \| a > b and a, b belong to {1, 2, 3}}
C.	{(a,b) \| a <= b and a, b belong to {1, 2, 3}}
D.	{(a,b) \| a = b and a, b belong to {1, 2, 3}}
Answer» B. {(a,b) \| a > b and a, b belong to {1, 2, 3}}

Discussion

4.	Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, N_r) on A and the number of functions (say, N_f) from A to A?
A.	number of relations
B.	number of functions
C.	the element set
D.	number of subsets of the relation
Answer» B. number of functions

Discussion

5.	Let S be a set of n>0 elements. Let be the number B_r of binary relations on S and let B_f be the number of functions from S to S. The expression for B_r and B_f, in terms of n should be ____________
A.	n<sup>2</sup> and 2(n+1)<sup>2</sup>
B.	n<sup>3</sup> and n<sup>(n+1)</sup>
C.	n and n<sup>(n+6)</sup>
D.	2<sup>(n*n)</sup> and n<sup>n</sup>
Answer» E.

Discussion

6.	Consider the relation: R (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R is _________
A.	not equivalence relation
B.	an equivalence relation
C.	transitive and asymmetry relation
D.	reflexive and antisymmetric relation
Answer» C. transitive and asymmetry relation

Discussion

Explore topic-wise MCQs in Discrete Mathematics.

Determine the characteristics of the relation aRb if a2 = b2.

Let R1 be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:i. An element a in A is related to an element b in B (under R1) if a * b is divisible by 3.

Consider the binary relation, A = {(a,b) | b = a 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?

Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A?

Let S be a set of n>0 elements. Let be the number Br of binary relations on S and let Bf be the number of functions from S to S. The expression for Br and Bf, in terms of n should be ____________

Consider the relation: R (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R is _________

Determine the characteristics of the relation aRb if a² = b².

Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:
i. An element a in A is related to an element b in B (under R₁) if a * b is divisible by 3.

Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, N_r) on A and the number of functions (say, N_f) from A to A?

Let S be a set of n>0 elements. Let be the number B_r of binary relations on S and let B_f be the number of functions from S to S. The expression for B_r and B_f, in terms of n should be ____________