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**Exercises with the Material Conditional**

Kareem Khalifa Department of Philosophy Middlebury College

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Overview Surprise! Brief Digression: “Unless” Exercises

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**Unless The rule: translate “unless” as “v” But why?**

“p unless q” = “p if not q” Ex. You will be free of logic on Friday, unless you’re in Section X. If you’re not in Section X, you’ll be free of logic on Friday. So “p unless q” = “~q p” Next step: show that “~q p” = “p v q”

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**“p unless q” = “~q p” = “p v q”**

T F F T T T F T T F

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**Unless: Recap It is natural to interpret “p unless q” as “p, if not q”**

“p, if not q” is equivalent to “p v q” So “p unless q” is naturally interpreted as “p v q”

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**But doesn’t ‘unless’ entail an exclusive “or”?**

Often, but not always. Ex. “The picnic will be held unless it rains.” What happens if it rains? Exclusive “or/unless”: no picnic. However, the speaker may mean that it will be held indoors, in which case, there is a picnic and it rains. Inclusive “or/unless.”

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Exercise A2 A X T F F

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Exercise A9 A (B Z) T (T F) T (F) F

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**Exercise A19 [(A & X) C] [(A X) C]**

[(T & F) T] [(T F) T] [(F) T] [(F) T] [T] [T] T

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**Exercise A24 [(A & X) Y] [(A X) & (A Y)]**

[(T & F) F] [(T F) & (T F)] [(F) F] [(F) & (F)] [T] [F] F

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Exercise C2 If Argentina mobilizes then either Brazil will protest to the UN or Chile will call for a meeting of all Latin American states. A (B v C)

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Exercise C4 If Argentina mobilizes then Brazil will protest to the UN, and Chile will call for a meeting of all Latin American states. (A B) & C

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Exercise C8 If Argentina does not mobilize then either Brazil will not protest to the UN or Chile will not call for a meeting of all the Latin American states. ~A (~B v ~C)

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Exercise C21 Argentina’s mobilizing is a sufficient condition for Brazil to protest to the UN. A B

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Exercise C22 Argentina’s mobilizing is a necessary condition for Chile to call for a meeting of all the Latin American states. CA

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Exercise C24 If Argentina mobilizes and Brazil protests to the UN, then either Chile or the Dominican Republic will call for a meeting of all the Latin American states. (A&B) (C v D)

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Section 1.1. Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: a) The Moon is made of green.

Section 1.1. Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: a) The Moon is made of green.

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