1
GATE CSE 2002
+2
-0.6
The binary relation $$S = \phi$$ (emply set) on set A = {1, 2, 3} is
A
Neither reflexive nor symmetric
B
Symmetric and reflexive
C
Transitive and reflexive
D
Transitive and symmetric
2
GATE CSE 2001
+2
-0.6
Consider the following statements:

S1: There exist infinite sets A, B, C such that
$$A\, \cap \left( {B\, \cup \,C} \right)$$ is finite.
S2: There exist two irrational numbers x and y such that (x + y) is rational.
Which of the following is true about S1 and S2?

A
Only S1 is correct
B
Only S2 is correct
C
Both S1 and S2 are correct
D
None of S1 and S2 is correct
3
GATE CSE 2001
+2
-0.6
Let $$f:\,A\, \to B$$ be a function, and let E and F be subsets of A. Consider the following statements about images.

$$S1:\,f\,\left( {E\, \cup \,F} \right)\, = \,f\left( E \right)\, \cup \,f\,\left( F \right)$$
$$S2:\,f\,\left( {E\, \cap \,F} \right)\, = \,f\left( E \right)\, \cap \,f\,\left( F \right)$$
Which of the following is true about S1 and S2?

A
Only S1 is correct
B
Only S2 is correct
C
Both S2 and S2 are correct
D
None of S1 and S2 is correct
4
GATE CSE 2000
+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
$$S\,\, \notin \,P(S)$$
GATE CSE Subjects
EXAM MAP
Medical
NEET