Question

Say true or false.

If X = {$1,2,3$}, all possible subsets of X are {$1$}, {$2$}, {$3$}, {$1,2$}, {$1,3$}, {$2,3$}, {$1,2,3$}.

• A. True
• B. False

Answer 1

The correct option is B False

$\text{Subsets of X containing zero element=}\varphi$
$\text{Subsets of X containing one element}=\left\{1\right\},\left\{2\right\},\left\{3\right\}$
$\text{Subsets of X containing two elements}=\{1,2\},\{2,3\},\{1,3\}$
$\text{Subsets of X containing three elements}=\{1,2,3\}$
Hence, all possible subsets of X are
$\varphi ,\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{2,3\},\{1,3\},\{1,2,3\}$