Define P(A)= set of all subsets of A.
S(A) = A U {A}.

Let 0=empty set;

a. Compute S(0), S(S(0)), S(S(S(0))), S(S(S(S(0, ...
b. Compute P(0), P(P(0)), P(P(P(0))),

Depict the above up to at least 5 levels, by placing the S-series in the middle as main bone, and growing the flesh by depicting elements of P's around the main bone.

Set Theorists call this the Cumulative hierarchy of sets. Describe it!

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

is there supposed to be a picture here?