Equating Truth Table Expressions: A NAND Solution

[hholzer]

Wasn't sure of where the most appropriate place would be for this post.

If you have a truth table, say for inclusive OR, then you get a
sums-of-products expression:

(A * B^c) + (A^c * B) + (A * B)

From this, how could I arrive at the following:

A + B = ((A + B)^c)^c = (A^c * B^c)^c
Then, we can say A + B is equivalent to:
(A NAND A) NAND (B NAND B)

Hence, we can write inclusive OR in terms of
three NANDS. In short: how can I equate
(A * B^c) + (A^c * B) + (A * B) to
(A^c * B^c)^c

I've played around with it a bit but I'm not
hitting upon anything.

 

[Stephen Tashi]

If you have a truth table, say for inclusive OR, then you get a
sums-of-products expression:

(A * B^c) + (A^c * B) + (A * B)

No, a truth table is a table, not a logical expression. The values in a truth table are "True" or "False" ( 0 or 1 if you use that notation).

In short: how can I equate
(A * B^c) + (A^c * B) + (A * B) to
(A^c * B^c)^c

I think what you want to do is show the equivalence of A + B with (A^c*B^c)^c.

If you want to use truth tables, you would have to write a truth table for those two expressions showing all possible cases of the truth or falsity of A and B.

If you want to use the rules for manipulating logical variables, begin with the rule that (P*Q)^c = P^c + Q^c. Apply that rule to (A^c*B^c)^c