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 correct simplified circuit diagram for the logical statement $[\{q \wedge (\sim q \vee r)\} \wedge \{\sim p \vee (p \wedge \sim r)\}] \vee (p \wedge r)$ where $p, q, r$ represent switches $S_1, S_2, S_3$ respectively.

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

If $(p \wedge \sim r) \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of $p, q, r$ are respectively:

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

Which of the following is $NOT$ equivalent to $p \rightarrow q$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module