Construct the truth table for: p → (q → p) – Class 12 Mathematics | ConceptFirst

Miscellaneous Exercise 1 · Q159

p \to (q \to p)

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

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Build the table for $p\to(q\to p)$ over all combinations of $p,q$ :

$p=T,q=T$ : $q\to p = T\to T = T$ ; $p\to(q\to p) = T\to T = T$ .

$p=T,q=F$ : $q\to p = F\to T = T$ ; $p\to(q\to p) = T\to T = T$ .

$p=F,q=T$ : $q\to p = T\to F = F$ ; $p\to(q\to p) = F\to F = T$ . …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL2 marks
$[(p\rightarrow q)\wedge q]\rightarrow p$
›Reveal solutionSolution

Build the columns $p\to q$ , $(p\to q)\wedge q$ , then $\to p$ .

$p$ $q$ $p\to q$ $(p\to q)\wedge q$ $[(p\to q)\wedge q]\to p$
T T T T T
T F F F T

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CBSE 2023Set ANNUAL2 marksMCQ
$p \wedge q$
(a) T, T
(b) T, F
(c) F, T
(d) F, F
›Reveal solutionSolution

$p\to q$ is false only when $p=T,\ q=F$ ; check this satisfies $p\wedge q=F$ .

…

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