GATE CSE 2015 Set 2 | Mathematical Logic Question 17 | Discrete Mathematics

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

-0.3

Consider the following two statements.

$$S1:$$ If a candidate is known to be corrupt, then he will not be elected
$$S2:$$ If a candidate is kind, he will be elected

Which one of the following statements follows from $$S1$$ and $$S2$$ as per sound inference rules of logic?

If a person is known to be corrupt, he is kind

If a person is not known to be corrupt, he is not kind

If a person is kind, he is not known to be corrupt

If a person is not kind, he is not known to be corrupt

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

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Consider the following statements:
P: Good mobile phones are not cheap
Q: Cheap mobile phones are not good
L: P implies Q
M: Q implies P
N: P is equivalent to Q

Which of the following about L, M, and N is Correct?

Only L is TRUE.

Only M is TRUE.

Only N is TRUE.

L, M and N are TRUE.

GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

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Consider the statement
"Not all that glitters is gold"
Predicate glitters$$(x)$$ is true if $$x$$ glitters and
predicate gold$$(x)$$ is true if $$x$$ is gold.

Which one of the following logical formulae represents the above statement?

$$\forall x:\,glitters\,\left( x \right) \Rightarrow \neg gold\left( x \right)$$

$$\forall x:\,gold\left( x \right) \Rightarrow glitters\left( x \right)$$ v

$$\exists x:\,gold\left( x \right) \wedge \neg glitters\left( x \right)$$

$$\exists x:\,glitters\,\left( x \right) \wedge \neg gold\left( x \right)$$

GATE CSE 2012

MCQ (Single Correct Answer)

-0.3

What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"

$$\exists x\left( {real\left( x \right) \vee rational\left( x \right)} \right)$$

$$\forall x\left( {real\left( x \right) \to rational\left( x \right)} \right)$$

$$\exists x\left( {real\left( x \right) \wedge rational\left( x \right)} \right)$$