Help with some boolean algebra/basic electronics?

Dsf

New member
Please help! I'm havin trouble with these 3 problems.

1. Prove this statement:

xy'z' + x'yz' = [(xy'z')' (x'yz')']'

2. I need a boolean expression in sum of products form and a block diagram for this problem:

Circuit = 1 under the following conditions:
1.
x = 0
y = 0
z = 1

2.
x=1
y=1
z=0

I got the truth table and my answer is X'Y'Z + XYZ'
I'm not sure if its possible to simplify it anymore, but I need help in drawing a circuit for it (with logic gates).

The second problem is the same format as above but this time the output is 0 when:

1.
x=1
y=1
z=1

2.
x=0
y=0
z=0

3.
x=1
y=0
z=0

For my answer I got X'Y'Z' + XY'Z' + XYZ. If somebody could simplify and draw a circuit diagram or explain what gates are needed, I would really appreciate it.
 
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