1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
The following resolution rule is used in logic programming. Derive clause $$\left( {P \vee Q} \right)$$ from clauses $$\left( {P \vee R} \right)$$, $$\left( {Q \vee \neg R} \right)$$.

Which of the following statements related to this rule is FALSE?

A
$$\left( {\left( {P \vee R} \right) \wedge \left( {Q \vee \neg R} \right)} \right) \Rightarrow \left( {P \vee Q} \right)$$ is logically valid
B
$$\left( {P \vee Q} \right) \Rightarrow \left( {\left( {P \vee R} \right) \wedge \left( {Q \vee \neg R} \right)} \right)$$ is logically valid
C
$$\left( {P \vee Q} \right)$$ is satisfiable if and only if $${\left( {P \vee R} \right) \wedge \left( {Q \vee \neg R} \right)}$$ is satisfiable
D
$$\left( {P \vee Q} \right) \Rightarrow $$ FALSE if and only if both $$P$$ and $$Q$$ are unsatisfiable
2
GATE CSE 2000
MCQ (Single Correct Answer)
+2
-0.6
Let $$a, b, c, d$$ be propositions. Assume that the equivalences $$a \leftrightarrow \left( {b \vee \neg b} \right)$$ and $$b \leftrightarrow c$$ hold. Then the truth value of the formulae $$\left( {a\, \wedge \,b} \right) \to \left( {\left( {a \wedge c} \right) \vee d} \right)$$ is always
A
True
B
False
C
Same as truth value of $$b$$
D
Same as truth value of $$d$$
3
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is false? Read $$ \wedge $$ as AND, $$ \vee $$ as OR, $$ \sim $$ as NOT, $$ \to $$ as one way implication and $$ \leftrightarrow $$ two way implication.
A
$$\left( {\left( {x \to y} \right) \wedge x} \right) \to y$$
B
$$\left( {\left( { \sim x \to y} \right) \wedge \left( { \sim x \to \sim y} \right)} \right) \to x$$
C
$$\left( {x \to \left( {x \vee y} \right)} \right)$$
D
$$\left( {\left( {x \vee y} \right) \leftrightarrow \left( { \sim x \to \sim y} \right)} \right)$$
4
GATE CSE 1995
MCQ (Single Correct Answer)
+2
-0.6
If the proposition $$\neg p \Rightarrow q$$ is true, then the truth value of the proposition $$\neg p \vee \left( {p \Rightarrow q} \right)$$ where $$'\neg '$$ is negation, $$' \vee '$$ is inclusive or and $$' \Rightarrow '$$ is implication, is
A
true
B
multiple-valued
C
false
D
cannot be determined
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