Question 1167141
<pre>
U = {x ∈ Z | 0 ≤ x ≤ 20} = {0,1,2,3,...,20};

A = set of all even integers = {{{...-6,-4,-2,0,2,4,6,...}}};

B= set of all prime numbers = {{{2,3,5,7,11,13,17,19,...}}};

C = set of all numbers coprime with 2 = {{{3,5,7,9,11,...}}};

{y ∈ U | y= 2z + 3, for some z∈Z} 

To do the last one:

{{{0<=2z + 3<=20}}}

Solve for z in the middle.
Subtract 3 from all three sides:

{{{-3<=2z<=17}}}

Divide all three sides by 2

{{{-1.5<=z<=8.5}}}

Since z is an integer,

{{{-1<=z<=8}}} = {-1,0,1,2,3,...,8}, substitute each 
in 2z+3:

{y ∈ U | y = 2z + 3, for some z ∈ Z} = {1,3,5,7,...,19}

Edwin</pre>