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

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

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

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

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

Therefore.,

$\red{ Number \:of \:subsets } \\\green { = \{2\},\{5\},\{2,5\}, \{ \:\} }$

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