Show that the following four conditions are equivalent(i) A ⊂ B(ii) – InterviewSolution

InterviewSolution

1.

Show that the following four conditions are equivalent(i) A ⊂ B(ii) A – B=φ(iii) A ∪ B = B(iv) A ∩ B A.

Answer»

(i) ⇔ (ii):

A⊂B ⇔ All elements of A are in B ⇔ A – B = φ

(ii) ⇔ (iii):

A-B = φ⇔ All elements of A are in B ⇔ A∪B = B

(iii) ⇔(iv)

A∪B = B ⇔ All elements of A are in B ⇔ All elements of A are common in A and B.

⇔ A∩B = A

∴ All the four given conditions are equivalent.

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