1
GATE CSE 1996
+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
$$\left( {\left( {x \vee y} \right) \leftrightarrow \left( { \sim x \to \sim y} \right)} \right)$$
2
GATE CSE 1995
+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
3
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
4
GATE CSE 1990
+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
$$\left( {\left( {{\rm P} \Rightarrow R} \right) \vee \left( {Q \Rightarrow R} \right)} \right) \Rightarrow \left( {\left( {\left( {{\rm P} \vee Q} \right) \Rightarrow R} \right)} \right)$$
GATE CSE Subjects
EXAM MAP
Medical
NEET