For any two sets A and B, show that the following statements are …

Question

For any two sets A and B, show that the following statements are equevalent:
$\text{A}-\text{B}=\phi.$

✓

Answer

We new show that (2) ⇒ (3)
So assume that $\text{A - B}=\phi$
To show: $\text{A}\cup\text{B}=\text{B}$
$\because$ Every element of A is an element of B $[\because\text{A}-\text{B}=\phi$ only when ther is some element in A which is not in B$]$
So $\text{A}\subset\text{B}$ and therefore $\text{A}\cup\text{B}=\text{B}$
So (2) ⇒ (3) is true.

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