How to check whether A EX-NOR(BC) =(A EX-NOR B) (A EX-NOR C) ?

Question

Taking A=0, LHS= B'+C'

and RHS= B'C'

Taking A=1 ,LHS=BC

RHS= BC

Now for A=1 it is satisfied while for A=0 not satisfied so does the identity hole or not ?

Comments

For a equality to be true it must hold true for every value that the variables involved can possibly take.

Answer 1

method (1)

LHS=A x-nor (BC)=ABC+(A)'(BC)'=ABC+(A)'(B'+C')=ABC+A'B'+A'C'

RHS=(AB+A'B')(AC+A'C')=ABC+A'B'C' 

SO, LHS!=RHS

method(2)

A	B	C	Ax-nor(BC)	(A xnor B)(A xnor C)
0	0	0	1	1
0	0	1	1	0
0	1	0	1	0
0	1	1	0	0
1	0	0	0	0
1	0	1	0	0
1	1	0	0	0
1	1	1	1	1

so from this truth table also LHS != RHS