For all sets A, B and C, if A , then A - Vidyadip

Question

For all sets A, B and C, if $\text{A}\subset\text{B},$ then $\text{A}\cap\text{C}\subset\text{B}\cap\text{C}$

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Answer

True.
Let $\text{x}\in\text{A}\cap\text{C}$
$\Rightarrow \text{x}\in \text{A}$ and $\text{x}\in\text{C}$
$\Rightarrow \text{x}\in\text{B}$ and $\text{x}\in\text{C}\ \big[\because \text{A}\subset\text{B}\big]$
$\Rightarrow \text{x}\in(\text{B}\cap\text{C})$
$\Rightarrow (\text{A}\cap\text{C})\subset(\text{B}\cap\text{C})$
Hence, given statement is true.

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