Test: Set Theory & Algebra- 2 - Computer Science Engineering (CSE) MCQ

Since group is abelian so it is commutative as well as associative.

A relation which is symmetric and transitive, need not foe reflexive relation.
(i) R = {}; on the set A = {a, b}. The relation R is symmetric and transitive but not reflexive.
(ii) R = {(a, a), (b, b)}; on the set A = {a, b}.
The relation R is symmetric, transitive and also reflexive.
∴ A relation is transitive and symmetric relation but need not be reflexive relation.

Representing above set using Venn diagram as follows:

∴ By Venn diagram,

In option (c), the set of all strings over a finite alphabet ∑ doesn’t forms a group under concatenation because the inverse of a string doesn’t exist with respect to concatenation.

The relation R doesn’t contain (4, 4), so R is not reflexive relation.
Since relation R contains ( 1 ,1 ) , (2, 2) and (3, 3).
Therefore, relation R is also not irreflexive.
That R is transitive, can be checked by systematically checking for all (a, b) and (b, c) in R, whether (a, c) also exists in R.

φ always present in any powerset of a set and φ is the only common element between P(S) and P(P(S)

According to inclusion - exclusion formula:

PL = students who have taken programming.
DS = Students who have taken Data structures.
CO = Students who have taken Computer Organization.
So, the number of students who have taken atleast 1 of the 3 courses is given by:
= 125 + 85 + 65 - 50 - 35 - 30 + 15
= 175
Therefore, the number of students who have not taken any of the 3 courses is 
= Total students-students taken atleast 1 course 
= 200 - 175 = 25

P Δ Q = PQ' + PQ
where Δ is symmetric difference between P and Q.
1.

2.

∴ R is not antisymmetric.
R is neither-symmetric nor anti-symmetric.

Let n = 2. There are only 2 onto functions as shown below:


The number of onto functions from a set A with m elements to set B with n elements where n < m is given by