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Mathematics

Assertion (A) : Let A = {x | x + 3 = 0, x ∈ N}, B = {x | x ≤ 3, x ∈ W} then A ∩ B = B.

Reason (R) : For any set A, A ∩ Φ = Φ.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Sets

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Answer

Given : A = {x | x + 3 = 0, x ∈ N}, B = {x | x ≤ 3, x ∈ W}

⇒ x + 3 = 0

⇒ x = -3

Since, x ∈ N. So, A = {}

Whole number = {0, 1, 2, 3, ……………..} and x ≤ 3

So, B = {0, 1, 2, 3}

A ∩ B means this set contains elements common to both A and B.

⇒ A ∩ B = {}

⇒ A ∩ B ≠ B

So, assertion (A) is false.

For any set A, A ∩ Φ = Φ

The intersection of any set with the empty set is always the empty set.

So, reason (R) is true.

Hence, option 4 is the correct option.

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