Priority of logical connectors
high to low:
Implication:
In
is called the hypothesis is called the conclusion
Ways to read
implies - If
then if only if whenever is sufficient for is necessary for
The converse of
The negation of
The contrapositive of
Equivalence:
is equivalent to is necessary and sufficient for if and only if iff precisely when
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
When
Logically Equivalent
Two statements
, are logically equivalent if is always true for all possibilities of atomic statement truth value combinations
Example:
To verify, we check
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | F | F | T |
| F | F | T | T | T |