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Question

# List alt possible subsets of the set given set. a. $G = Q$ L. $K = \{ 6 \}$ c. $I = \{ 6,7 \}$ . d. $J = \{ 6,7,8 \}$ e. $K = \{ 6,7,8,9 \}$

Solution

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We know that for a set of $n$ element, the total number of subset is $2^n.$ For example $A=\{a, b, c\}, d\}$ is a set of 4 elements. so the possible subsets are $2^{\wedge} 4=16$ and these are

$\phi,\{a\},\{b\},\{c\},\{d\},$

$\{a, b\},\{a, c\},\{a, d\}, \{b, c\},\{b, d\}, \{c, d\}$

$\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},$

$\{a, b, c, d\}$

$G=\phi$. Then $G$ is the only subset of $G$.

$K=\{6\}$. Then $\phi, \{6\}$ is the only subsets of $K.$

$I=\{6, 7\}$. Then $\phi, \{6\},\{7\}, \{6,7\}$ are the subsets of $I.$

$J=\{6, 7, 8\}$. Then

$\phi, \{6\},\{7\}, \{8\}$

$\{6,7 \},\{6, 8 \}, \{7,8\}$

$\{6,7,8,\}$

are the subsets of $J.$

$J=\{6, 7, 8, 9\}$. Then

$\phi, \{6\},\{7\}, \{8\},{9}$

$\{6,7 \},\{6, 8 \}, \{6,9\},\{7,8\},\{7,9\} ,\{8,9\}$

$\{6,7,8\}, \{6,7,9\},\{6,8,9\}, \{7,8,9\}$

$\{6,7,8,9\}$

are the subsets of $J.$

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