Obtain the complement function of YSolutionDemorgans law is

Obtain the complement function of Y

Demorgans law is used to complement a function:

complement of union of 2 sets equal to intersection of complement and vice versa is called demorgans law.

example:

rules of demorgans law;

1.(xy)\'=x\'+y\';

2.(a\')\'=a\'\'=a;

F=a(b\'+c)

F\'=[a(b\'+c)]\'

example 2:

Y=ab+a\'c+bc\'

Y\'=[ab+a\'c+bc\']\'=[ab+a\'c+(bc\')\']=(ab+ac\')\'(bc\')\'

[(ab)+(ac)][b+c]=(ab)(a\'c)[b+c]=(a+b)(a+c)(b+c)

(a+b)(a+c)(b+c)

[aa+ac+ab+bc](b+c)

[0+ac+ab+bc](b+c)

abc+acc+abb+abc+ybc+bcc

a\'b\'c\'+a\'(0)+a(b\')+ab\'c+(b\')c\'+b\'(0)

a\'b\'c\'+ab\'+ab\'c+bz\'

Y\'=b\'(a\'c\'+a+ac+c\')