please do solve this problem for the part b This question he

please do solve this problem for the part (b)!!!!!!!!!!!!!!!

This question helps with understanding the proof 10.3.27. Let S = {a,b,c). ta, b, c a) List the elements of P(S) b) Define a function f : S P(S) of your own choice, and determine the subset So = {x e sla ¢ f(x)). Demonstrate that So range(f).

Solution

given S={a,b,c}

if a set \'S\' has \'n\' elements then it\'s powerset will have 2^n elements in it

here n=3 then p(s) will have 2^3 =8 elements

p(s) = { {} , {a} ,{b} ,{c} ,{a,b}, {b,c} {a,c} ,{a,b,c} }

for 2nd part

range means  set of all second elements of ordered pairs ( p(s)-coordinates)

x has to belongs to S but not p(s)

we ca have (a,{}) (b,{}) ,(c,{}) ({a,b} ,{} ) ({b,c} ,{} ) ({a,c} ,{} )