Maharashtra State BoardHSC Arts 12th Board Exam
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Construct the truth table of the following statement pattern. [p → (q → r)] ↔ [(p ∧ q) → r] - Mathematics and Statistics

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Sum

Determine whether the following statement pattern is a tautology, contradiction or contingency:

[p → (q → r)] ↔ [(p ∧ q) → r]

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Solution

p q r q → r p → (q → r) p ∧ q (p ∧ q) → r [p → (q → r)] ↔ [(p ∧ q) → r]
T T T T T T T T
T T F F F T F T
T F T T T F T T
T F F T T F T T
F T T T T F T T
F T F F T F T T
F F T T T F T T
F F F T T F T T

All the entries in the last column of the above truth table are T.
∴ [p → (q → r)] ↔ [(p ∧ q) → r] is a tautology.

Concept: Statement Patterns and Logical Equivalence
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 7.4 | Page 33

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