DISCRETE MATHEMATICS 1. Translate each of the following statements as a compound

Question

DISCRETE MATHEMATICS

1. Translate each of the following statements as a compound propositional formula using correct logical connectives. You must clearly define the propositional variables atoms) you used in your translations, as in class. Define them at the bottom of the page (a) Canadians are not fairly represented in the parliament when votes do not count equally or voter turnout is low Compound proposition (b) The government is committed to improving the voting system only if votes count equally Compound proposition (c) In order for voter turnout to be low, it is sufficient that votes do not count equally Compound proposition (d) Canadians will be fairly represented in the parliament if and only if the govern- ment is committed to improving the voting system and voter turnout is high Compound proposition (e) Unless voter turnout is high, Canadians will not be fairly represented in the parliament Compound proposition

Explanation / Answer

a) The given proposition in symbolic form is (~q v r) => ~p

b) The given proposition in symbolic form is s => q

c) The given proposition in symbolic form is ~q => r

d) The given proposition in symbolic form is p <=> (s ^ ~r)

e) The given proposition in symbolic form is ~(~r) => ~p. That is, r=> ~p

Atomic statements are: p = Canadians are fairly represented, q = votes count equally, r = voter turnout is low, s = Govt. is committed to improving the voting system

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