1
GATE CSE 1994
True or False
+2
-0
Let $$p$$ and $$q$$ be propositions. Using only the truth table decide whether $$p \Leftrightarrow q$$ does not imply $$p \to \sim q$$ is true or false.
A
TRUE
B
FALSE
2
GATE CSE 1994
+1
-0.3
Let A and B be any two arbitrary events, then, which one of the following is true?
A
$$P\,(A\, \cap \,B)\, = \,P\,(A)\,P\,(B)$$
B
$$P\,(A\, \cup \,B)\, = \,P\,(A)\, + \,P\,(B)$$
C
$$P\,(A\,\left| {B) = \,} \right.P\,(A\, \cap \,B)\,P\,(B)$$
D
$$P\,(A\, \cup \,B)\, < \,\,P\,(A)\, + \,P\,(B)$$
3
GATE CSE 1994
+2
-0.6
Some group (G, o) is known to be abelian. Then, which one of the following is true for G?
A
$$g = {g^{ - 1}}\,$$ for every $$g\, \in \,G$$.
B
$$g = {g^{ 2}}\,$$ for every $$g\, \in \,G$$.
C
$${(goh)^2} = \,{g^2}\,o\,\,{h^2}$$ for every g, $$h\, \in \,G$$.
D
G is of finite order.
4
GATE CSE 1994
+2
-0.6
The number of substrings (of all length inclusive) that can be formed from a character string of length $$n$$ is
A
$$n$$
B
$${n^2}$$
C
$${{n\left( {n - 1} \right)} \over 2}$$
D
$${{n\left( {n + 1} \right)} \over 2}$$
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