Logical Connectives
Turning 'if', 'only if', 'unless', 'either-or' and 'neither-nor' into conditionals, using the contrapositive, and telling the two valid inferences (modus ponens, modus tollens) from the two fallacies (affirming the consequent, denying the antecedent).
What you will be able to do
- Translate each connective into a P → Q conditional with the antecedent and consequent identified.
- Write the contrapositive and use it as an equivalent of the original.
- Apply modus ponens and modus tollens as the only two valid one-step inferences.
- Reject affirming-the-consequent and denying-the-antecedent conclusions.
What is inside this lesson
- 1Everything reduces to 'if P then Q'
- 2Translating the connectives
- 3The contrapositive and the two valid moves
- 4Worked examples
- 5Common mistakes
- 6Quick revision
- 7Practice
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Everything reduces to 'if P then Q'
Many reasoning questions give a rule in words and a fact, and ask what validly follows. Almost every connective can be rewritten as a conditional P → Q — read as 'if P, then Q', where P is the antecedent and Q the consequent.
Once it is in that form, only a small set of moves is valid. The whole skill is (1) translating correctly and (2) applying only the valid moves.
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