Truth functions
SO- ∴
&&- ∧
!!- ¬
∨ (double the key below backspace)
~=- ≈
Truth functional connectives, if applied to functions α and β which have the same truth value, will result with propositions with the same truth value.
Unary truth functional connective - e.g. connective ¬
Not a unary truth functional connective - e.g. Trump believes that
To test if a connective is truth functional, we create 2 propositions with the same truth value - α and β - and apply the connective to them, if the result is the propositions with different truth values, then the connective is not truth functional
Unary tautology - result is true in all situations
Truth tables for wff’s
| P | Q | ¬ | (P | ∧ | ¬ | Q) |
|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| (5) | (1) | (4) | (3) | (2) |
Expressive adequacy
If you like this course you’re a logician
If the two wffs have the same truth tables they are equivalent to each other (≈ ); they are the same semantically speaking (i.e. the result is the same truth wise).
Study slide three of chapter 12