Q.7 Using the truth table, show that the statement pattern p→(q→ p) is a tautology.

Answer: All entries in the last column are T, so p→(q→ p) is a tautology. p q q→ p p→(q→ p) TTTT TFTT FTFT FFTT Since every entry in the last column is T, the statement pattern is a tautology.

Chapter: Mathematical Logic· Mathematics & Statistics Part 1

Using the truth table, show that the statement pattern \(p\to(q\to p)\) is a tautology.

Q.7 Using the truth table, show that the statement pattern \(p\to(q\to p)\) is a tautology.

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

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Answer: All entries in the last column are T, so \(p\to(q\to p)\) is a tautology.

\(p\)	\(q\)	\(q\to p\)	\(p\to(q\to p)\)
T	T	T	T
T	F	T	T
F	T	F	T
F	F	T	T

Since every entry in the last column is T, the statement pattern is a tautology.

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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Using the truth table, show that the statement pattern \(p\to(q\to p)\) is a tautology.

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