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Question Number 159071 by physicstutes last updated on 12/Nov/21

Determine the cardinality and power set of B = {{a,b,c},{d,e},{f,g,h,i}

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{and}\:\mathrm{power} \\ $$$$\mathrm{set}\:\mathrm{of} \\ $$$${B}\:=\:\left\{\left\{{a},{b},{c}\right\},\left\{{d},{e}\right\},\left\{{f},{g},{h},{i}\right\}\right. \\ $$

Answered by Rasheed.Sindhi last updated on 12/Nov/21

cardinality of B=3, because B has 3 members:(1) {a,b,c} (2) {d,e} (3){f,g,h,i} Let they′re named as X,Y & Z Power Set of B P(B)={φ,{X},{Y},{Z},{X,Y}{X,Z}{Y,Z}{X,Y,Z}}

$$\mathrm{cardinality}\:\mathrm{of}\:\mathrm{B}=\mathrm{3},\:\mathrm{because}\:\mathrm{B} \\ $$$$\mathrm{has}\:\mathrm{3}\:\mathrm{members}:\left(\mathrm{1}\right)\:\left\{{a},{b},{c}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left\{{d},{e}\right\}\:\left(\mathrm{3}\right)\left\{{f},{g},{h},{i}\right\} \\ $$$$\mathrm{Let}\:\mathrm{they}'\mathrm{re}\:\mathrm{named}\:\mathrm{as}\:\mathrm{X},\mathrm{Y}\:\&\:\mathrm{Z} \\ $$$$\mathrm{Power}\:\mathrm{Set}\:\mathrm{of}\:\mathrm{B} \\ $$$$\mathrm{P}\left(\mathrm{B}\right)=\left\{\phi,\left\{\mathrm{X}\right\},\left\{\mathrm{Y}\right\},\left\{\mathrm{Z}\right\},\left\{\mathrm{X},\mathrm{Y}\right\}\left\{\mathrm{X},\mathrm{Z}\right\}\left\{\mathrm{Y},\mathrm{Z}\right\}\left\{\mathrm{X},\mathrm{Y},\mathrm{Z}\right\}\right\} \\ $$

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