For any two sets A and B, show that the following statements are equiv – InterviewSolution

InterviewSolution

1.

For any two sets A and B, show that the following statements are equivalent: A ⊂ B

Answer»

To show that the following four statements are equivalent, we need to show that 1⇒2, 2⇒3, 3⇒ 4, 4⇒1

We first show that 1⇒ 2

Now A–B = {xϵ A: x ∉ B} .As A ⊂ B,

∴ Each element of A is an element of B,

∴ A–B = ϕ

Hence we proved 1⇒ 2.

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