Question

State whether for all sets $A,B$ and $C$, if $A\subset C$ and $B\subset C$, then $A\cup B\subset C$ is true or false. Justify your answer.

Answer 1

Let $x\in A\cup B$

$\Rightarrow x\in A$ or $x\in B$

$\Rightarrow x\in C$ or $x\in C$ $\{\because A\subset CandB\subset C\}$

$\Rightarrow x\in C$

$\Rightarrow A\cup B\subset C$

Hence, the given statement is true.