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in Sets, Relations and Functions by (28.9k points)
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For any two sets of A and B, prove that: 

A’ ∪ B = U A ⊂ B

1 Answer

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Best answer

To show: A⊂B 

⇒ x ∉ A 

⇒ x ϵ A and A ⊂ U 

⇒ x ϵ A 

⇒ x ϵ (A’ ∪ B) [∵ U = A’∪ B] 

⇒ x ϵ A’ or x ϵ B 

But, 

x ∉ A’, 

∴ x ϵ B 

Thus, 

x ϵ A ⇒ x ϵ B 

This is true for all x ϵ A 

∴ A ⊂ B

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