1
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Let p and q be the following propositions:

p: Fail grade can be given.

q: Student scores more than 50% marks.

Consider the statement: “Fail grade cannot be given when student scores more than 50% marks.”

Which one of the following is the CORRECT representation of the above statement in propositional logic?

A

q → ¬ p

B

q → p

C

p → q

D

¬ p → q

2
GATE CSE 2016 Set 2
Numerical
+1
-0
Consider the following expressions:
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(i)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ false
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(ii)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$Q$$
$$\,\,\,\,\,\,\,\,\,\,\,$$ $$(iii)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ true
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(iv)$$ $$\,\,\,\,\,\,\,\,\,\,\,$$ $$P∨Q$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(v)$$ $$\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\neg QVP$$

The number of expressions given above that are logically implied by $$P \wedge \left( {P \Rightarrow Q} \right)$$) is _____________.

3
GATE CSE 2016 Set 1
Numerical
+1
-0
Let $$p,q,r,s$$ represent the following propositions.

$$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$
$$q:\,\,\,x$$ is a composite number
$$r:\,\,\,x$$ is a perfect square
$$s:\,\,\,x$$ is a prime number

The integer $$x \ge 2$$ which satisfies $$\neg \left( {\left( {p \Rightarrow q} \right) \wedge \left( {\neg r \vee \neg s} \right)} \right)$$ is ______________.

4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
In a room there are only two types of people, namely Type $$1$$ and Type $$2.$$ Type $$1$$ people always tell the truth and Type $$2$$ people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following “The result of the toss is head if and only if I am telling the truth.”

Which of the following options is correct?

A
The result is head
B
The result is tail
C
If the person is of Type $$2,$$ then the result is tail
D
If the person is of Type $$1,$$ then the result is tail
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