# Set Theory and Algebra MCQ - Sets

61:

A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE?

 A. R is not an equivalence relation B. R is an equivalence relation having one equivalence class C. R is an equivalence relation having two equivalence classes D. R is an equivalence relation having three equivalence classes Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
62:

Let P(S) denote the power set of set S. Which of the following is always TRUE ?

 A. P(P(S)) = P(S) B. P(S)  ∩ S = P (S) C. P(S)  ∩ P(P(S))  = [ φ ] D. S ∉ P(S) Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here:
63:

If R be a symmetric and transitvie relation on a set A, then

 A. R is reflexive and hence an equivalence relation B. R is reflexive and hence a partial order C. R is not reflexive and hence not an equivalence relation D. None of these Answer Report Discuss Option: D Explanation : Click on Discuss to view users comments. Write your comments here:
64:

The number of binary relations on a set with n elements is

 A. n2 B. 2n^2 C. 2n D. None of these Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Write your comments here:
65:

If A and B be sets and AC and Bc denote the complements of the sets A and B, then set (A — B)  (B — A)  (A   ∩ B) is equal to

 A. A ∪ B B. Ac ∪ Bc C. A ∩ B D. Ac ∩ Bc Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Write your comments here: ∪ (B — A) ∪ (A   ∩ B) is equal to '>