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Chapter: Mathematical Logic· Mathematics & Statistics (Commerce) Part 1

Determine whether the following statement pattern is tautology, contradiction or contingency.\([(p\wedge q)\vee(\sim p)]\vee[p\wedge(\sim q)]\)

Q.2 (A) (i) Determine whether the following statement pattern is tautology, contradiction or contingency.
\([(p\wedge q)\vee(\sim p)]\vee[p\wedge(\sim q)]\)

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Answer: Tautology

Truth table:

\(p\)\(q\)\(p\wedge q\)\(\sim p\)\((p\wedge q)\vee(\sim p)\)\(\sim q\)\(p\wedge(\sim q)\)\([(p\wedge q)\vee(\sim p)]\vee[p\wedge(\sim q)]\)
TTTFTFFT
TFFFFTTT
FTFTTFFT
FFFTTTFT

All the entries in the last column are T, so the given statement pattern is a tautology.

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