Question

Question 9 X.X = X True False Question 10 The Boolean function Flx, y, z) = (y + x)(y + x)(y'+z) is equivalent to: yz y'z + xyz + xyz O y'z+xz X

Answer 1

Question 9:

x.x = x

Answer: True

Question 10:

The Boolean function F(x,y,z) = (y+x)(y+x¹)(y¹+z) is equivalent to:

Answer: yz

Explanation:

(y+x)(y+x¹)(y¹+z)

= (y.y+yx¹+xy+x.x¹)(y¹+z)

= (y+yx¹+xy+0)(y¹+z) [ since y.y = y and x.x¹ = 0 ]

= (y+xy)(y¹+z) [ since y+yx¹ = y ]

= (yy¹+yz+xy.y¹+xyz)

= (0+yz+0+xyz) [ since y.y¹ = 0 ]

= (yz(1+x)

= yz [ since 1+x = 1 ]