1
GATE CSE 1993
MCQ (Single Correct Answer)
+1
-0.3
The proposition $$p \wedge \left( { \sim p \vee q} \right)$$ is
A
a tautology
B
$$\Leftrightarrow \left( {p \wedge q} \right)$$
C
$$\Leftrightarrow \left( {p \vee q} \right)$$
D
a contradiction
2
GATE CSE 1993
Subjective
+5
-0
Show that proposition $$C$$ is a logical consequence of the formula $$A \wedge \left( {A \to \left( {B \vee C} \right) \wedge \left( {B \to \sim A} \right)} \right)$$ using truth tables.
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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