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 &gt;= b and a, b belong to {1, 2, 3}}
B. {(a,b) | a &gt; b and a, b belong to {1, 2, 3}}
C. {(a,b) | a &lt;= 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 &gt; b and a, b belong to {1, 2, 3}}
Discussion
4.

Let A be a set of k (k&gt;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?

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&gt;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 ____________

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&gt;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