Show that the following four conditions are ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 61 of 73

Marks: +1, -0

Show that the following four conditions are equivalent :

(i) A ⊂ B (ii) A – B = f (iii) A ∪ B = B (iv) A ∩ B = A

Solution:

(i) ⇒ (ii)

A – B = {x : x ∈ A and x ∉ B}

Since A ⊂ B

∴ A – B = f

(ii) ⇒ (iii)

A – B = f ⇒ A ⊂ B ⇒ A ∪ B = B

(iii) ⇒ (iv)

A ∪ B = B ⇒ A ⊂ B ⇒ A ∩ B = A

(iv) ⇒ (i)

A ∩ B = A ⇒ A ⊂ B

Thus (i) ⇔ (ii) ⇔ (iii) ⇔ (iv).

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