Question

Please simplify the following Boolean expression to its simplest form: F(x, y, z) = y'z + x'yz + xyz?

Please simplify the following Boolean expression to its simplest form: F(x, y) = (x + y)(xy)’ + ((x + y)(xy)’)’?

Answer 1

F(x, y, z) = y'z + x'yz + xyz
           = y'z + (x'+x)yz
           = y'z + (1)yz
           = y'z + yz
           = (y'+y)z
           = (1)z
           = z


F(x, y) = (x + y)(xy)’ + ((x + y)(xy)’)’
        = (x + y)(xy)' + ((x + y)(xy)’)’
        = (x + y)(xy)' + (x + y)' + (xy)
        = (x + y)(x' + y') + (x + y)' + (xy)
        = xx' + yx' + xy' + yy' + (x + y)' + (xy)
        = 0 + yx' + xy' + 0 + (x + y)' + (xy)
        = yx' + xy' + (x + y)' + (xy)
        = yx' + xy' + x'y' + xy