Question

Qn from class11 probability:

If P(A)=P(B), show that A=B.

(will be marked as brainliest for perfect answer)✌​

Answer 1

Step-by-step explanation:

Let x ∈ A

⇒ x ∈ P(A)

But,

Given, P(A) = P(B)

⇒ x ∈ P(B)

⇒ x ∈ B

So,

x ∈ A ⇒ x ∈ B

∴ A ⊂ B     ------ (1)

Now,

Let x ∈ B

⇒ x ∈ P(B)

But,

Given,

P(A) = P(B)

⇒ x ∈ P(A)

⇒ x ∈ A

So,

x ∈ B ⇒ x ∈ A

∴ B ⊂ A      ------ (2)

Since A ⊂ B and B ⊂ A

∴ A = B

Hope it helps!