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Prove the following logic property using a Truth Table (perfect induction). What is this property called?
x + y * z = (x + y)(x + z)
My Answer:
Distributive Property?
Truth table.
By truth table I get: \(\displaystyle \bar{x}yz + x\bar{y}z + xyz\) which becomes z + z + xyz ?
Am I doing this wrong? Why am I not getting x + yz?
should I use algebraic manipulation?
x + yz = (x + y)(x + z)
x + yz = xx + xz + xy + yz
x + yz = x + xz + xy + yz
now what?
x + y * z = (x + y)(x + z)
My Answer:
Distributive Property?
Truth table.
x y z f
[0]0 0 0 0
[1]0 0 1 0
[2]0 1 0 0
[3]0 1 1 1
[4]1 0 0 0
[5]1 0 1 1
[6]1 1 0 0
[7]1 1 1 1
By truth table I get: \(\displaystyle \bar{x}yz + x\bar{y}z + xyz\) which becomes z + z + xyz ?
Am I doing this wrong? Why am I not getting x + yz?
should I use algebraic manipulation?
x + yz = (x + y)(x + z)
x + yz = xx + xz + xy + yz
x + yz = x + xz + xy + yz
now what?
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