Lecture 1/14/08

Lecture 1/14/08 - Being a citizen is a necessary condition...

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Disjunction (or, unless) o Dallas will win = D o Buffalo will win = B o D v B Conditional o You earn exactly 900 points = N o You get some form of A = A o If you earn exactly 900 pts, then you will get some form of A N A o Statement following ‘if’ is antecedent, statement following ‘then’ is consequent (does not apply to ‘only if’) o Jim can vote = V o Jim is a citizen = C o Jim can vote if Jim is a citizen C V NOT TRUE o Jim can vote only if Jim is a citizen V C TRUE o A sufficient condition is a condition that suffices for something else (but it may not be necessary) Earning 800 points is sufficient for passing the class, but it is not necessary o A necessary condition is a condition that is required for something else (but it may not be sufficient) Hydrogen is necessary for water (but it is not sufficient)
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Unformatted text preview: Being a citizen is a necessary condition for voting (but it is not sufficient) o Sufficient ⊃ Necessary • Biconditional o If and only if o Iff o Is necessary and sufficient for o You will get a P in this class if and only if you earn a C- or better You get a P = P You earn a C- or better = C P ≡ C • Translating Compound Statements o I’ll buy an Xbox 360, and either a PSP or Nintendo DS X = I’ll buy and Xbox 360 P = I’ll buy a PSP N = I’ll buy a Nintendo DS X, and either P or N X • (P v N) o The car runs well and the motorcycle runs well, but you should be careful if you take the boat out C = the car runs well M = the motorcycle runs well Y B C and M, but Y if B (C • M) • (B ⊃ Y)...
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  • Spring '08
  • churchland
  • Jim, Necessary and sufficient condition, If and only if, Nintendo DS, citizen VC TRUE, Translating Compound Statements

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Lecture 1/14/08 - Being a citizen is a necessary condition...

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