Discrete Mathematics For each case prove A B a A x x2 x

Discrete Mathematics

For each case, prove A = B.

a. A = {x | x² = x} B = {x | x² = x}

b. A = {x | 15 divides x}

c. B = {x | 3 divides x and 5 divides x}

Solution

a> For A & B, x² =x => x²-x =0 => x(x-1)=0 => x=0 or x=1 and 0 and 1 both are integers as well as rational number.

So A= {0,1} and B ={0,1}

Hence A=B