1
GATE CSE 2000
MCQ (Single Correct Answer)
+2
-0.6
Let P(S) denote the power set of a set S. Which of the following is always true?
A
$$P\,(P(S))\, = P\,(S)$$
B
$$P\,(S)\, \cap \,P\,(P\,(S)) = \{ \emptyset \} $$
C
$$P\,(S)\,\, \cap \,\,S = P\,(S)$$
D
$$S\,\, \notin \,P(S)$$
2
GATE CSE 2000
MCQ (Single Correct Answer)
+2
-0.6
A relation R is defined on the set of integers as zRy if f (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 1 equivalence class
C
R is an equivalence relation having 2 equivalence classes
D
R is an equivalence relation having 3 equivalence classes
3
GATE CSE 1999
Subjective
+2
-0

(a) Mr. X claims the following:
If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof.

"From xRy, using symmetry we get yRx. Now because R is transitive, xRy and yRx togethrer imply xRx. Therefore, R is reflextive."


Briefly point out the flaw in Mr. X' proof.

(b) Give an example of a relation R which is symmetric and transitive but not reflexive.

4
GATE CSE 1998
MCQ (Single Correct Answer)
+2
-0.6
The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is
A
Reflexive, symmetric and transitive
B
Neither reflexive, nor irreflexive but transitive
C
Irreflexive, symmetric and transitive
D
Irreflexive and antisymmetric
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