Page "Logical biconditional" Paragraph 3

In the propositional interpretation, a ⇔ b means that a implies b and b implies a ; in other words, that the propositions are equivalent, that is to say, either true or false at the same time.

This does not mean that they have the same meaning.

Example: " The triangle ABC has two equal sides ", and " The triangle ABC has two equal angles ".

The antecedent is the premise or the cause and the consequent is the consequence.

When an implication is translated by a hypothetical ( or conditional ) judgment the antecedent is called the hypothesis ( or the condition ) and the consequent is called the thesis.