Construct the truth table for the following statement pattern: $[(p \rightarrow q) \land q] \rightarrow p$

| p | q | $p\rightarrow q$ | $(p\rightarrow q)\land q$ | $[(p\rightarrow q)\land q]\rightarrow p$ | |---|---|---|---|---| | T | T | T | T | T | | T | F | F | F | T | | F | T | T | T | F | | F | F | T | F | T | The final column has both T and F values (not all T, not all F). > [!ANSWER] Final column: T, T, F, T — the pattern is a contingency.

Construct the truth table for the following statement pattern: [(p arrow q) land q] arrow p

Exercise 1.2 · Q43

[(p \rightarrow q) \land q] \rightarrow p

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✓ Free question

p	q	$p\rightarrow q$	$(p\rightarrow q)\land q$	$[(p\rightarrow q)\land q]\rightarrow p$
T	T	T	T	T
T	F	F	F	T
F	T	T	T	F
F	F	T	F	T

The final column has both T and F values (not all T, not all F).

✓Final answer

Final column: T, T, F, T — the pattern is a contingency.

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
F T T T F
F F T F T

✓Final answer
$p,q=$
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 $p\wedge q=F$ .

$p\to q$ is F only in the case $p=T$ and $q=F$ . Checking $p\wedge q$ for $p=T,q=F$ : $T\wedge F = F$ , which matches the given $p\wedge q=F$ . So both conditions hold simultaneously only for $p=T,\ q=F$ .

✓Final answer
$(b) T, F$

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Q.Construct the truth table for the following statement pattern: $[(p \rightarrow q) \land q] \rightarrow p$

Concept understanding — Statement Patterns and Truth Tables

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

Q.Construct the truth table for the following statement pattern: [(p→q)∧q]→p[(p \rightarrow q) \land q] \rightarrow p[(p→q)∧q]→p

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Q.Construct the truth table for the following statement pattern: $[(p \rightarrow q) \land q] \rightarrow p$

Unlock everything free for 14 days