# Simple truth table

1. Aug 20, 2011

### autre

I need to find the formula involving $\neg$, $\wedge$ or $\vee$ for the following truth table with the variables P and Q:

P Q formula
F F F
F T T
T F T
T T F

The closest I've gotten is something like P$\vee(\neg$P$\wedge$Q) which clearly doesn't work for the last row. Any ideas?

2. Aug 20, 2011

### MisterX

That's the truth table for "exclusive or".

¬P∧Q is only true with P = F and Q = T. (line 2)

P∧¬Q is only true with P = T and Q = F. (line 3)

These are what are known as minterms. Minterms are expressions using only conjunction and negation (∧ and ¬), which are true for the inputs from one line of the truth table with a true output. Each input should be represented in the minterm.

The disjunction (∨) of all minterms will be an expression that corresponds to the truth table.

Last edited: Aug 20, 2011