LogicLesson 2 of 2

Necessity, Sufficiency & Applied Logic

Formulas

Inclusion-Exclusion (Venn)

|A∪B|=|A|+|B|−|A∩B|Both=|A|+|B|−|those with at least one|

Part 1 of 1

Affirming the Consequent & Venn

Affirming the consequent is invalid: P→Q and Q is true does NOT prove P.

The correct inference from "Q is true" alone: nothing about P. P might or might not be true.

Venn diagram procedure

Label circles A and B
Write the total and "neither" count
|A ∪ B| = total − neither
|A ∩ B| = |A| + |B| − |A ∪ B|

Always draw it. Always.

Worked example

"Interest rates drop → equity rises." Equity rose today. Does NOT mean rates dropped — other causes exist. This is affirming the consequent.

Venn: 40 people, 25 English, 18 French, 8 neither. |E∪F| = 32. Both = 25+18−32 = 11.

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