Truth Tables

Steps on constructing a truth table:

1. Determine number of unique sentence letters (n)

2. Create n columns at the left, one for each unique sentence letter

3. Create 2n rows

4. Determine all possible truth value combinations for columns at the left

5. Determine truth values for each connective in the sentence, working from smallest to largest

Conjunction Φ & Ψ
- For a conjunction to be true, both conjuncts must be true.

Disjunction Φ v Ψ
- For a disjunction to be false, both disjuncts must be false.

Conditional Φ --> Ψ
- A conditional is true no matter what if it has a false antecedent and a true consequent

Biconditional Φ <--> Ψ
- For a biconditional to be true, both sides must have the same truth value.

Validity:
- If the TT contains a line where all premises are true, yet the conclusion is false, then the sequence is invalid.

No premises:
- In TT's with no premises, then there must be no line with a false conclusion.

Tautology:
- a phrase or expression in which the same thing is said twice in different words.

Inconsistent:
- a sentence that only has Fs in its column of a TT is inconsistent.

Contingent:
- a sentence that is neither tautologous nor inconsistent.

Indirect TT:
- a shorter way to find invalidating assignments then a TT.