1
GATE CSE 2004
+2
-0.6
The following is the incomplete operation table of a 4-element group. The last row of the table is
A
$$\matrix{ c & a & e & b \cr }$$
B
$$\matrix{ c & b & a & e \cr }$$
C
$$\matrix{ c & b & e & a \cr }$$
D
$$\matrix{ c & e & a & b \cr }$$
2
GATE CSE 2004
+2
-0.6
The inclusion of which of the following sets into

S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4},
{1, 2, 3, 4, 5} }
Is necessary and sufficient to make S a complete lattice under the partial order defined by set containment?

A
{1}
B
{1}, {2, 3}
C
{1}, {1, 3}
D
{1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}
3
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
4
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
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
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