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Question Number 117567 by bounhome last updated on 12/Oct/20
give A={a,b,c,d,e}; n(p(A))=?
$${give}\:{A}=\left\{{a},{b},{c},{d},{e}\right\};\:{n}\left({p}\left({A}\right)\right)=? \\ $$$$\:\:\: \\ $$
Answered by mr W last updated on 12/Oct/20
C_0 ^5 +C_1 ^5 +C_2 ^5 +C_3 ^5 +C_4 ^5 +C_5 ^5 =2^5 =32  ⇒n(p(A))=32
$${C}_{\mathrm{0}} ^{\mathrm{5}} +{C}_{\mathrm{1}} ^{\mathrm{5}} +{C}_{\mathrm{2}} ^{\mathrm{5}} +{C}_{\mathrm{3}} ^{\mathrm{5}} +{C}_{\mathrm{4}} ^{\mathrm{5}} +{C}_{\mathrm{5}} ^{\mathrm{5}} =\mathrm{2}^{\mathrm{5}} =\mathrm{32} \\ $$$$\Rightarrow{n}\left({p}\left({A}\right)\right)=\mathrm{32} \\ $$
Commented by bounhome last updated on 13/Oct/20
and p(A)=?
$${and}\:{p}\left({A}\right)=? \\ $$
Commented by mr W last updated on 13/Oct/20
all 32 subsets of A:  {0}  {a},{b},...,{e}  {a,b},{a,c},...,{d,e}  ...  {a,b,c,d,e}
$${all}\:\mathrm{32}\:{subsets}\:{of}\:{A}: \\ $$$$\left\{\mathrm{0}\right\} \\ $$$$\left\{{a}\right\},\left\{{b}\right\},…,\left\{{e}\right\} \\ $$$$\left\{{a},{b}\right\},\left\{{a},{c}\right\},…,\left\{{d},{e}\right\} \\ $$$$… \\ $$$$\left\{{a},{b},{c},{d},{e}\right\} \\ $$

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