Determine whether or not the following expressions are valid, i. e., whether the left- and right-hand sides represent same function. use truth table method for b, c and boolean algebra for a. draw the logic circuits for the left hand side expression for a, b,c

(a) x1'x3 + x1x2x3' + x1'x2 + x1x2' = x2'x3 + x1x3' + x2x3' + x1'x2x3

(b)x1x3' +x2x3 +x2'x3' =(x1 +x2' +x3)(x1 +x2 +x3')(x1' +x2 +x3')

(c)(x1 +x3)(x1' +x2' +x3')(x1' +x2)=(x1 +x2)(x2 +x3)(x1' +x3')