Let X = {0, 1, 2}. List the elements of each of the following sets: a. {z : z = 2x and x ∈ X} b. {z : z = x + y where x ∈ X and y ∈ X}

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a: let's iterate over the elements in the set x to make new set

$2*0=0$ , $2*1=2$ , $2*2=4$

it means set is {0, 2, 4}

b: let's iterate over the elements in the set x to make new set

$0+0=0, 0+1=1,0+2=2,$

$1+1=2,1+2=3,2+2=4$

it means set is {0, 1, 2, 3, 4}