JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of JEE Mathematics questions?

JEE Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

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Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

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

Choose the correct answer:

Explanation

Step 1: Expression ko rearrange karna

Hum expression ko do parts mein dekh sakte hain:

(p \wedge \sim q) \vee [(\sim p \wedge q) \vee (\sim p \wedge \sim q)]

Step 2: Distributive Law apply karna

Brackets ke andar waale part mein se $(\sim p)$ common lete hain:

(\sim p \wedge q) \vee (\sim p \wedge \sim q) \equiv \sim p \wedge (q \vee \sim q)

Step 3: Identity Law ka use

Hum jaante hain ki $(q \vee \sim q)$ hamesha True (T) hota hai:

\sim p \wedge T \equiv \sim p

Step 4: Final Simplify

Ab bacha hua expression hai:

(p \wedge \sim q) \vee \sim p

Ise simplify karne ke liye distributive law ka ulta use karte hain:

(\sim p \vee p) \wedge (\sim p \vee \sim q)

Kyunki $(\sim p \vee p)$ hamesha True (T) hota hai:

T \wedge (\sim p \vee \sim q) \equiv \sim p \vee \sim q

Conclusion:

Diyagaya statement $(\sim p) \vee (\sim q)$ ke barabar hai.

Correct Option: (1)

Choose the correct answer:

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