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 |
Option: C Explanation : Click on Discuss to view users comments. |
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) |
Option: C Explanation : Click on Discuss to view users comments. |
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 |
Option: D Explanation : Click on Discuss to view users comments. |