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Mathematical Reasoning
medium
The statement $p \rightarrow (q \rightarrow p)$ is equivalent to
A
$p \rightarrow (p \rightarrow q)$
B
$p \rightarrow (q\, \vee \, p)$
C
$p \rightarrow (q\, \wedge p)$
D
$p \rightarrow (p \leftrightarrow q)$
(AIEEE-2008)
Solution
As $\mathrm{q} \rightarrow \mathrm{p}=\sim \mathrm{q} \vee \mathrm{p}$ and $\mathrm{p} \rightarrow(\mathrm{q} \rightarrow \mathrm{p})=\sim \mathrm{p} \mathrm{v} \sim \mathrm{q} \vee \mathrm{p}$
The truth value of $p \rightarrow(q \rightarrow p)$ is a tautology
and truth value of $\sim \mathrm{pv} \sim \mathrm{q}$ v $\mathrm{p}$ is also a tautology
Hence $p \rightarrow(q \rightarrow p)=\sim p \vee \sim q \vee p$
Standard 11
Mathematics
