- #1

Back2College

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## Homework Statement

Using only NOT and XOR, construct a compound statement having the same truth table as:

(a)

*p*OR

*q*

(b)

*p*AND

*q*

## Homework Equations

XOR is "exclusive OR."

*p*XOR

*q*= (

*p*OR

*q*) AND NOT (

*p*AND

*q*).

I have been working under the assumption that I can use parentheses.

## The Attempt at a Solution

I know the truth tables for (

*p*OR

*q*) and (

*p*AND

*q*) are TTTF and TFFF, respectively. So, either three Trues and one false or one True and three Falses.

However, when I use only NOT and XOR I always get two Trues and two Falses. So far this has been the case no matter which combination I try or how many XORs I string together. It's always some combination of two Trues and two Falses.

Can anyone give me a hint?

Thanks.