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GATE CSE 1992
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-0.3
Which of the following predicate calculus statements is/are valid?
A
$$\left( {\forall \,x} \right){\rm P}\left( x \right) \vee \left( {\forall \,x} \right)Q\left( x \right) \to \left( {\forall \,x} \right)$$
$$\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\}$$
B
$$\left( {\exists \,x} \right){\rm P}\left( x \right) \wedge \left( {\exists \,x} \right)Q\left( x \right) \to \left( {\exists \,x} \right)$$
$$\left\{ {{\rm P}\left( x \right) \wedge Q\left( x \right)} \right\}$$
C
$$\left( {\forall \,x} \right)\,\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\} \to \left( {\forall \,x} \right)\,\,$$
$${\rm P}\left( x \right) \vee \left( {\forall \,x} \right)\,\,Q\left( x \right)$$
D
$$\left( {\exists \,x} \right)\,\,\left\{ {{\rm P}\left( x \right) \vee Q\left( x \right)} \right\} \to \sim \left( {\forall \,x} \right)\,\,$$
$$\,{\rm P}\left( x \right) \vee \left( {\exists \,x} \right)Q\left( x \right)$$
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