Question

list all the subsets of a set containing prime factors of 100​

Answer 1

$Given \: number \:100$

2 | 100

________

2 | 50

________

5 | 25

________

**** 5

$Prime \: Factorisation \: of \: 100 = 2^{2} \times 5^{2}$

$\blue { Prime \:factors\: of \: 100 } \green {= \{2,5\} }$

$Number \:of \: elements \:in \:the \:set (n) = 2$

$Number \:of \: subsets = 2^{n} \\= 2^{2} \\= 4$

Therefore.,

$\red { List\: of \: all \:the \: subsets \: of \:a }\\\red{ set \: containing \:prime \:factors \:of \:100 }\\\green { \{2\} , \{5\}, \{2,5\} , \{ \: \} }$

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