Finding a formula for the truth table F, T, T, F

  • Context: Undergrad 
  • Thread starter Thread starter autre
  • Start date Start date
  • Tags Tags
    Table Truth table
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 3K views
autre
Messages
116
Reaction score
0
I need to find the formula involving [itex]\neg[/itex], [itex]\wedge[/itex] or [itex]\vee[/itex] 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[itex]\vee(\neg[/itex]P[itex]\wedge[/itex]Q) which clearly doesn't work for the last row. Any ideas?
 
Physics news on Phys.org
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: