Use a truth table to demonstrate the validity of x+yz=(x+y)(x+z)

Answer 1

Here's the truth table demonstrating x + yz = (x + y)(x + z):

x y z yz x + yz x + y x + z (x+y)(x+z)
0	0	0	0	0	0	0	0
0	0	1	0	0	0	1	0
0	1	0	0	0	1	0	0
0	1	1	1	1	1	1	1
1	0	0	0	1	1	1	1
1	0	1	0	1	1	1	1
1	1	0	0	1	1	1	1
1	1	1	1	1	1	1	1

The columns x + yz and (x+y)(x+z) are identical for all input combinations, proving the identity is valid. This is the distributive law for Boolean algebra.