Question

F(X,Y) = (X'+Y) . (X+Y) . (X'+X)

Answer 1

Sadd DV fccvdvffvbhredghhgrhhhhrfhjgfg

Answer 2

Theorem 1: Let (B,+, . , ‘, 0,1) be a Boolean Algebra. Then the following hold:

a) x+x=x and x.x=x for all x in B

b) x+1=1 and 0.x=0 for all x in B

c) x+(xy)=x and x.(x+y)=x for all x and y in B

Proof:

a) x = x+0 Identity laws

= x+xx’ Complementation laws

= (x+x).(x+x’) because + is distributive over .

= (x+x).1 Complementation laws

= x+x Identity laws

x = x.1 Identity laws

= x.(x+x’) Complementation laws

= x.x +x.x’ because + is distributive over .

= x.x+0 Identity laws

= x.x

b) x+1 =x+(x+x’) Complementation laws

= (x+x)+x’ + is associative

= x+x’ using (a)

= 1 Complementation laws

0.x =(x’.x).x Complementation laws

= x’.(x.x) . is associative

= x’.x using (a)

=0 Complementation laws

c) x+(xy) = x.1+x.y Identity laws

=x.(1+y) because + is distributive over .