3 votes 3 votes $R=P\left ( P\left ( P\left ( \phi \right ) \right ) \right )$ $T=P\left ( P\left ( \left \{ 1,2 \right \} \right ) \right )$ What is cardinality of set $S$, where $S=R\times T$ Set Theory & Algebra discrete-mathematics set-theory + – srestha asked Dec 28, 2017 srestha 546 views answer comment Share Follow See 1 comment See all 1 1 comment reply LeenSharma commented Jan 7, 2018 reply Follow Share https://www.facebook.com/photo.php?fbid=164865770949256&set=gm.728807463991133&type=3&theater&ifg=1 1 votes 1 votes Please log in or register to add a comment.
Best answer 4 votes 4 votes $R=P(P(P(\phi ))) = P(P(2^0)) = P(2^1)=2^2=4 \\T=P(P(\{ 1,2\})=P(2^2)=2^4=16 \\S=R\ \times T\\S=4 \ \times 16=\color{RED}{64} $ saxena0612 answered Dec 28, 2017 selected Dec 30, 2017 by joshi_nitish saxena0612 comment Share Follow See all 3 Comments See all 3 3 Comments reply srestha commented Dec 30, 2017 reply Follow Share @ saxena0612 what elements of $P\left ( \Phi \right )$ ? $P\left ( \Phi \right )$=$\left \{ \Phi ,\left \{ \Phi \right \} \right \}$ rt? Then why u take $P\left ( \Phi \right )=1?$ 0 votes 0 votes sourav. commented Dec 30, 2017 reply Follow Share srestha number of elements in $P(\phi)=2^{0}=1$ 0 votes 0 votes sourav. commented Dec 30, 2017 reply Follow Share Srestha your reasoning is correct for power set of $\left \{ \phi \right \}$ , but here we need to find power set of just $\phi$ 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes R=P(P(P(Ø)))=P(P(2^0))=P(P(1))=P(2^1)=P(2)=2^2=4 Similarly T=P(P{1,2}))=P(2^2)=P(4)=2^4=16 Hence S=R*T=4*16=64 Here POWER of set containg n element=P(N)= 2^n. DIBAKAR MAJEE answered Apr 27, 2020 DIBAKAR MAJEE comment Share Follow See all 0 reply Please log in or register to add a comment.