Let p, q, r be three statements,then [p right | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We analyze the logical expression $[p$ $\rightarrow (q$ $\rightarrow r)] \leftrightarrow [(p \wedge q)$ $\rightarrow r]$.First,consider the left s

Vedclass · Accepted Answer

a tautology.

Vedclass · Answer

(C) We analyze the logical expression $[p$ $ightarrow (q$ $ightarrow r)] \leftrightarrow [(p \wedge q)$ $ightarrow r]$.First,consider the left side: $p$ $ightarrow (q$ $ightarrow r)$.Using the implication law $A ightarrow B \equiv 
eg A \vee B$,we get:$p$ $ightarrow (q$ $ightarrow r) \equiv 
eg p \vee (
eg q \vee r)$.By the associative law,this is equivalent to $(
eg p \vee 
eg q) \vee r$.By De Morgan's law,$
eg p \vee 
eg q \equiv 
eg (p \wedge q)$.Thus,$p$ $ightarrow (q$ $ightarrow r) \equiv 
eg (p \wedge q) \vee r$.Again,using the implication law,$
eg (p \wedge q) \vee r \equiv (p \wedge q) ightarrow r$.Since both sides of the biconditional are logically equivalent,the expression $[p$ $ightarrow (q$ $ightarrow r)] \leftrightarrow [(p \wedge q)$ $ightarrow r]$ is always true.Therefore,it is a tautology.

Let $p, q, r$ be three statements,then $[p$ $\rightarrow (q$ $\rightarrow r)] \leftrightarrow [(p \wedge q)$ $\rightarrow r]$ is

Similar Questions

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

If $(p \wedge \sim q) \wedge r \to \sim r$ is $F$,then the truth value of $r$ is:

The statement $(p$ $\rightarrow (q$ $\rightarrow p))$ $\rightarrow (p$ $\rightarrow (p \vee q))$ is

The converse of $[p \wedge (\sim q)] \rightarrow r$ is

Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module