Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let F_1(A,B,C)=(A\wedge B)\vee [\sim C\wedge (A\vee B)]\vee \sim A and F_2(A,B)=(A\vee B)\vee(B\rightarrow \sim A) be two respective logical expressions. Then:
Option: 1 F_1 is not a tautology but F_2 is a tautology
Option: 2 F_1 is a tautology but F_2 is not a tautology
Option: 3 Both F_1 \text{and}F_2 are not tautologies
Option: 4 F_1 \text{and}F_2 both are tautologies

Answers (1)

best_answer

\begin{aligned} F_{1} &:(A \wedge \sim B) \vee[\sim C \wedge(A \vee B)] \vee \sim A \\ F_{2} &:(A \vee B) \vee(B \rightarrow \sim A) \\ F_{1} &:\{(A \wedge \sim B) \vee \sim A\} \vee[(A \vee B) \wedge \sim C] \\ &:\{(A \vee \sim A) \wedge(\sim A \vee \sim B)\} \vee[(A \vee B) \wedge \sim C] \\ &:\{t \wedge(\sim A \vee \sim B)\} \vee[(A \vee B) \wedge \sim C] \\ &:(\sim A \vee \sim B) \vee[(A \vee B) \wedge \sim C]\\ &:[(\sim A \vee \sim B) \vee(A \vee B)] \wedge[(\sim A \vee \sim B) \wedge \sim C] \end{aligned}

\\F_{1}:(\sim A \vee \sim B) \wedge \sim C \neq t(\text { tautology }) \\ F_{2}:(A \vee B) \vee(\sim B \vee \sim A)=t(\text { tautology })

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 response sheet errors: Delhi HC allows student to apply for JEE Adv, seeks NTA explanation
anam-khan

Four Kashmiri girls defy the odds, score 99+ percentile in JEE Main 2025
anam-khan

JEE, NEET, CUET coaching centres: Assam, Rajasthan have framed laws, but will they work?

Latest Question