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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 1990
MCQ (Single Correct Answer)
+2
-0.6
Indicate which of the following well-formed formula are valid:
A
$$\left( {\left( {{\rm P} \Rightarrow Q} \right) \wedge \left( {Q \Rightarrow R} \right)} \right) \Rightarrow \left( {{\rm P} \Rightarrow R} \right).$$
B
$$\left( {{\rm P} \Rightarrow Q} \right) \Rightarrow \left( { \sim P \Rightarrow \sim Q} \right)$$
C
$$\left( {{\rm P}\, \wedge \,\left( { \sim {\rm P}\,\,V \sim Q} \right)} \right) \Rightarrow Q\left( { \sim {\rm P} \Rightarrow \sim Q} \right)$$
D
$$\left( {\left( {{\rm P} \Rightarrow R} \right) \vee \left( {Q \Rightarrow R} \right)} \right) \Rightarrow \left( {\left( {\left( {{\rm P} \vee Q} \right) \Rightarrow R} \right)} \right)$$
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