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2 votes
2 votes
Construct the truth table for:

p → (q ∧ r)

The choices below represent the final column for the truth table. Identify the correct answer.

User SundayMonday
by
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1 Answer

11 votes
11 votes

You should know that

p ⇒ q ≡ ¬p ∨ q

so that

p ⇒ (q ∧ r) ≡ ¬p ∨ (q ∧ r)

Then making the truth table is simple:


\begin{array}{cccccc} p & q & r & \\eg p & q \land r & p \implies (q\land r) \\ T & T & T & F & T & T \\ T & T & F & F & F & F \\ T & F & T & F & F & F \\ T & F & F & F & F & F \\ F & T & T & T &  T & T \\ F & T & F & T & F &  T \\ F & F & T & T & F & T \\ F & F & F & T & F & T \end{array}

User Akhtar Munir
by
3.3k points