1
GATE CSE 1995
MCQ (Single Correct Answer)
+1
-0.3
The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is
A
$$2$$
B
$$4$$
C
$$8$$
D
None of the above
2
GATE CSE 1995
MCQ (Single Correct Answer)
+1
-0.3
Let $$R$$ be a symmetric and transitive relation on a set $$A$$. Then
A
$$R$$ is reflexive and hence an equivalence relation.
B
$$R$$ is reflexive and hence partial order.
C
$$R$$ is not reflexive and hence not an equivalence relation.
D
None of the above.
3
GATE CSE 1993
MCQ (Single Correct Answer)
+1
-0.3
Let $$S$$ be an infinite set and $${S_1},\,\,{S_2},....\,\,{S_n}$$ be sets such that $${S_1} \cup {S_2} \cup ....... \cup {S_n} = S$$. Then
A
At least one of the sets $${S_i}$$ is a finite set.
B
Not more than one of the sets $${S_i}$$ can be finite
C
At least one of sets $${S_i}$$ is infinite
D
Not more than one the sets $${S_i}$$ is an a infinite set.
4
GATE CSE 1993
MCQ (Single Correct Answer)
+1
-0.3
Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is
A
$${2^{{2^n}}}$$
B
$${2^{{n^2}}}$$
C
$${2^n}$$
D
$${n^2}$$
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