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
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
EXAM MAP
Joint Entrance Examination