1
GATE CSE 1999
Subjective
+5
-0
(a) Show that the formula $$\left[ {\left( { \sim p \vee Q} \right) \Rightarrow \left( {q \Rightarrow p} \right)} \right]$$ is not a tautology.

(b) Let $$A$$ be a tautology and $$B$$ be any other formula. Prove that $$\left( {A \vee B} \right)$$ is a tautology.

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 1992
Subjective
+5
-0
Uses Modus ponens $$\left( {A,\,\,A \to B\,|\,\, = B} \right)$$ or resolution to show that the following set is inconsistent:

(1) $$Q\left( x \right) \to P\left( x \right)V \sim R\left( a \right)$$
(2) $$R\left( a \right) \vee \sim Q\left( a \right)$$
(3) $$Q\left( a \right)$$
(4) $$ \sim P\left( y \right)$$
where $$x$$ and $$y$$ are universally quantifies variables, $$a$$ is a constant and $$P, Q, R$$ are monadic predicates.

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