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

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We know that for a set of nn element, the total number of subset is 2n.2^n. For example A={a,b,c},d}A=\{a, b, c\}, d\} is a set of 4 elements. so the possible subsets are 24=162^{\wedge} 4=16 and these are

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

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

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

G=ϕG=\phi. Then GG is the only subset of GG.

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

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

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

ϕ,{6},{7},{8}\phi, \{6\},\{7\}, \{8\}

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

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

are the subsets of J.J.

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

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

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

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

are the subsets of J.J.

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