The statement p → q → p → p → p ∨ q is :

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The statement

(p \to (q \to p)) \to (p \to (p \lor q))

is :

MathematicsMathematical ReasoningJEE MainJEE Main 2020 (05 Sep Shift 2)

Options:

A equivalent to $(p \land q) \lor (~ q)$
B a contradiction
C equivalent to $(p \lor q) \land (~ p)$
D a tautology

Solution:

2964 Upvotes Verified Answer

The correct answer is: a tautology

$p$	$q$	$q \to p$	$p \lor q$	$r : p \to (q \to p)$	$s : p \to (p \lor q)$	$r \to s$
$T$	$T$	$T$	$T$	$T$	$T$	$T$
$T$	$F$	$T$	$T$	$T$	$T$	$T$
$F$	$T$	$F$	$T$	$T$	$T$	$T$
$F$	$F$	$T$	$F$	$T$	$T$	$T$

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