1
GATE CSE 2023
MCQ (More than One Correct Answer)
+1
-0

Geetha has a conjecture about integers, which is of the form

$$\forall x\left( {P(x) \Rightarrow \exists yQ(x,y)} \right)$$,

where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?

A
$$\exists x\left( {P(x) \wedge \forall yQ(x,y)} \right)$$
B
$$\forall x\forall yQ(x,y)$$
C
$$\exists y\forall x\left( {P(x) \Rightarrow Q(x,y)} \right)$$
D
$$\exists x\left( {P(x) \wedge \exists yQ(x,y)} \right)$$
2
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+1
-0

Choose the correct choice(s) regarding the following propositional logic assertion S:

S : ((P ∧ Q)→ R)→ ((P ∧ Q)→ (Q → R))

A
The antecedent of S is logically equivalent to the consequent of S.
B
S is a tautology
C
S is a contradiction
D
S is neither a tautology nor a contradiction.
3
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Let p and q be two propositions. Consider the following two formulae in propositional logic.

S1 : (¬p ∧ (p ∨ q)) → q

S2 : q → (¬p ∧ (p ∨ q))

Which one of the following choices is correct?

A
Neither S1 nor S2 is a tautology.
B
S1 is not a tautology but S2 is a tautology.
C
Both S1 and S2 are tautologies.
D
S1 is a tautology but S2 is not a tautology.
4
GATE CSE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.33

The statement $(\neg p) \Rightarrow(\neg q)$ is logically equivalent to which of the statements below?

I. $\quad p \Rightarrow q$

II. $q \Rightarrow p$

III. $(\neg q) \vee p$

IV. $(\neg p) \vee q$

A
I only
B
I and IV only
C
II only
D
II and III only
GATE CSE Subjects
Software Engineering
Web Technologies
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