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Question

Choose the correct option.

Statement 1:(p q)( pq) is a fallacy.

Statement 2:(pq)( q p) is a tautology.

A
Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
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B
Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
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C
STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
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D
STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.
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Solution

If a logical compound statement always produces the truth (true value), then it is called a tautology.

The opposite of tautology is called fallacy or contradiction, in which the compound statement is always false.
Statement 1:

(p q)( pq)
Using Set Theory approach, this can be expressed as:
(PQc)(PcQ)



Clearly, the resultant is ϕ.
Hence, statement 1 is a fallacy.

Statement 2:

(pq)( q p)
Clearly, ( q p) is a contra-positive of (pq) and vice-versa.
Hence, statement 2 is a tautology.

Hence, the correct option is C Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.


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