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# T1.1 - -LOGICPropositions A proposition is a statement that...

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-LOGIC- Propositions A proposition is a statement that can, in principle, be determined to be either True (T) or False (F). -E.g. Today is Monday -Today is Tuesday -The square root of 4 is 2 -The square root of 4 is 1 -2 is even, and the square of two is even, and 3 is odd and the square of 3 is odd. -The Panthers can clinch a playoff berth with a win, plus a loss by the Rams, a loss or tie by the Saints and Bears, a win by the Seahawks and a tie between the Redskins and Cowboys. (Copied verbatim from the sports page 12/26/2004.) 1

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Non-propositions: What is today? Is today Monday? Show me some ID! 2x=4 x=y xy=yx!!! (depends on domain) This sentence is false (paradoxes are not propositions) 2
Propositions may be symbolized, hence the name “symbolic logic.” E.g. Today is Friday = p It is not Friday is denoted by -p. Not-p is a compound proposition. If p is T, then -p is F If p is F, then -p is T. This may be expressed concisely in a TRUTH TABLE: p -p T F F T 3

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Other kinds of sentences suggest other truth tables. Consider “Grass is ordinarily green and snow is ordinarily white ,” where the two underlined phrases are symbolized by p and q And p q p/\q T T T T F F F T F F F F Similarly for sentences like “The TV is broken or the fuse is defective ,” where the first proposition in the compound is p and the second is q: Or (Inclusive) p q p\/q T T T T F T F T T F F F 4
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T1.1 - -LOGICPropositions A proposition is a statement that...

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