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

Question

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

✓

Answer

True
Let $\text{x}\in\text{A}\cup\text{B}$
$\Rightarrow \text{x}\in \text{A}$ or $\text{x}\in\text{B}$
$\Rightarrow \text{x}\in\text{C}$ and $\text{x}\in\text{C}\ \big[\because \text{A}\subset\text{C and B}\subset\text{C}\big]$
$\Rightarrow \text{x}\in\text{C}$
$\Rightarrow \text{A}\cup\text{B}\subset\text{C}$
Hence, given statement is 'True'.

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