Question

Let A {p, q, {p}, {g}, {p, q}} (a) Is {p}C P(A)? (c) Is {{p}}€ P(A)? (d) Find all the three element sets in P(A) (b) Is {p} € P(A)? (e) Find all sets B such that B C A and {p, {p}}C B.

Answer 1

Given that A={p.4,{P3,{},{P.4}} PCA) it is the conection of our subsets of A. - S¢, $P3,$2},{{p}},{{2}}, {{P.2}},. Sp.9},{P.{p}},$2.{2}},{P. {P.2}}, $ 2,30}},{9,34}}, {2,98,9}}, {{p3,8233. $ 983, {0,2}},{843.22:2}}, {P.9,$3}, {P.2,5233,{p.99$223], § P, SP3,6213, SP.SP], 58a3}, se $23,58233, 123. $2,9}}, $2,383,923), 59,523, 58,933, § 5P3,521,521933, { 2,{2},{Pie}} $ 9,9,{e}, {a}}, { pia,&P3, 58.233 { piq;$23.Sp.z??, P3, şa3, SP.a}} SP.SP3,522, 22, 23}, {p.2,583,823. Spie}} :cand pra)=32 22.

@ is {p} C P (A): (Fase) {P] is an element of peas, so that {p} & PCA). o 25 {{1}} E PCA). Frene) Since spil is an element of PCA). © IS SP2 EPCA). (True) Because {p} is an element of PCA). @ {P.2,{p}}, { P,2,{2}}, {0,2,{0,2}}, {p.£p3, {a}}, { p. $23,32,433, $ p, 243, {1,2}}, { 2,383,8233, {7, 383, 88.43}, { $23, 323,8843}, Ş9,323,9€.2]

© we find all sets B such that BSA and {P. {p}} CB All the possible subsets Of A which gotiesfies the above condition are { P. $p3,9}, { P, 803, {2,4}} , { PSP3, {a}} Ş P.{83,2,8233, {p.5p),2.52,433, 32.503,323,32:41}, { P.83.2.522,50?