Question

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

Answer 1

$\because A\subset B$, if $a\in A\Rightarrow a\in B$

Let $x\in A\cup C$

$\Rightarrow x\in A$ or $x\in C$

$\Rightarrow x\in B$ or $x\in C$ $[\because A\subset B]$

$\Rightarrow x\in B\cup C$

$\therefore x\in A\cup C\subset B\cup C$

Hence, the given statement is true.