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JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Analyzing +4 | -1

Consider the two statements:

\left( {{S_1}} \right):\left( {p \to q} \right) \vee \left( { \sim q \to p} \right)

is a tautology

\left( {{S_2}} \right):\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \vee q} \right)

is a fallacy
then,

View answer and explanation

Correct option: C

Both

\left( {{S_1}} \right)

and

\left( {{S_2}} \right)

are true

Option C (Both (

S_1

) and (

S_2

) are true) is correct because

S_1

simplifies to a tautology and

S_2

simplifies to a fallacy.

More Questions from MATHEMATICAL REASONING

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p:A

q:A

man is rich
Then, the statement, "If a man is not happy, then he is not rich" is written as Consider the following compound statements.
(i) Mumbai is the capital of Rajasthan or Maharashtra.
(ii)

\sqrt{3}

is a rational or an irrational number.
(iii) 125 is a multiple of 7 or 8 .
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true? Let

p

q

be two Statements. Amongst the following, the Statement that is equivalent to

p \rightarrow q

{F_1}(A,\,B,\,C) = \left( {A \wedge \sim B} \right) \vee \left[ { \sim C \wedge \left( {A \vee B} \right)} \right] \vee \sim A

{F_2}(A,\,B) = \left( {A \vee B} \right) \vee (B \to \, \sim \,A)

be two logical expressions. Then, The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is : Suppose

p

: A natural number

n

q:

n

is not divisible by 2 , then the biconditional statement

p \Leftrightarrow q