JEE 2023 — Mathematics PYQ

Is sawal ko solve karne ke liye hum Boolean Algebra ke basic rules ya Truth Table ka upyog kar sakte hain.

1. Expression ko simplify karna:

Maan lijiye hamara expression hai:

Jahan,

Hum jaante hain ki $A\Rightarrow B$ ka matlab hota hai $(\sim A)\vee B$. Isliye:

Ab pura expression banta hai:

2. Implication rule apply karna:

Pura expression $X\Rightarrow Y$ ke roop mein hai, jise hum $(\sim X)\vee Y$ likh sakte hain:

De Morgan's Law apply karne par $(\sim (A\wedge B)=(\sim A)\vee (\sim B))$:

3. Associative aur Distributive property use karna:

Sari terms $\vee$ (OR) se judi hain, isliye hum brackets hata sakte hain:

Hum jaante hain ki:

• $(\sim p)\vee (\sim p)=\sim p$

• $q\vee (\sim q)=T$ (True/Tautology)

Toh expression banta hai:

Kyunki kisi bhi statement ka Tautology ($T$) ke saath OR karne par result hamesha True aata hai:

Correct Option: (1) a tautology