The statement p rightarrow (q rightarrow p) i | vedclass

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Question

(B) The given statement is $p$ $\rightarrow (q$ $\rightarrow p)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,we have:$p$ $\ri

Vedclass · Accepted Answer

$p \rightarrow (q \vee p)$

Vedclass · Answer

(B) The given statement is $p$ $\rightarrow (q$ $\rightarrow p)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,we have:$p$ $\rightarrow (q$ $\rightarrow p) \equiv \sim p \vee (\sim q \vee p)$.By the associative and commutative laws,this is equivalent to $(\sim p \vee p) \vee \sim q$,which simplifies to $T \vee \sim q = T$ (a tautology).Now,let us check option $B$: $p \rightarrow (q \vee p) \equiv \sim p \vee (q \vee p) \equiv (\sim p \vee p) \vee q \equiv T \vee q = T$.Since both expressions are tautologies,the statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to $p \rightarrow (q \vee p)$.

The statement $p$ $\rightarrow (q$ $\rightarrow p)$ is equivalent to

Similar Questions

Consider the following statements:
Statement $1$: If a quadrilateral is a square,then all of its sides are equal.
Statement $2$: If all the sides of a quadrilateral are equal,then it is a square.

The symbolic form of the following circuit is (where $p$ and $q$ represent switches $S_{1}$ and $S_{2}$ being closed respectively):

The number of values of $r \in \{p, q, \sim p, \sim q\}$ for which $((p \wedge q)$ $\Rightarrow (r \vee q)) \wedge ((p \wedge r)$ $\Rightarrow q)$ is a tautology,is:

The expression $\sim (p \vee q) \vee (\sim p \wedge q)$ is equivalent to:

If $p :$ It is raining today.
$q :$ $I$ go to school.
$r :$ $I$ will meet my friends.
$s :$ $I$ will go to watch a movie.
Then write the statement: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie' in symbolic form.

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