For any two sets A and B, if A∩X=B∩X=ϕ and A∪X=B∪X for some set X, then

# For any two sets A and B, if $\mathrm{A}\cap \mathrm{X}=\mathrm{B}\cap \mathrm{X}=\mathrm{\varphi }$ and $\mathrm{A}\cup \mathrm{X}=\mathrm{B}\cup \mathrm{X}$ for some set X, then

1. A

$\mathrm{A}-\mathrm{B}=\mathrm{A}\cap \mathrm{B}$

2. B

A=B

3. C

$\mathrm{B}-\mathrm{A}=\mathrm{A}\cap \mathrm{B}$

4. D

None of the above

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### Solution:

Given ,$\mathrm{A}\cap \mathrm{X}=\mathrm{B}\cap \mathrm{X}=\mathrm{\varphi }$

So, A and X, B and X are disjoint sets.

Also $\mathrm{A}\cup \mathrm{X}=\mathrm{B}\cup \mathrm{X}⇒\mathrm{A}=\mathrm{B}$

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