76 lines
1.7 KiB
Markdown
76 lines
1.7 KiB
Markdown
1. Which of the following English sentences express a proposition?
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(a) I think therefore I am.
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Proposition
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(b) Do as I say, not as I do!
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Command
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(c) Whenever the assignment x = y is executed, the value of y remains unaltered.
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Proposition
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(d) Write clearly and legibly.
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Command
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(e) How do you know your answers are correct?
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Question
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1. List the atomic propositions and connectives which appear in the following propositions and write down a well-formed formula for each one.
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(a) If it rains then I am going to get wet.
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Atomic Propositions:
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It rains
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I am going to get wet
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Connectives:
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If
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Then
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Formula: p => q
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(b) Increased spending overheats the economy.
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Atomic Propositions:
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Increased spending
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Overheats the economy
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Connectives:
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None, implied non-linguistic
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Formula: p => q
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(c) Increased spending coupled with tax cuts overheats the economy.
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Atomic Propositions:
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Increased spending
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There are tax cuts
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Overheated economy
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Connectives:
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Coupled with
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Formula: p ^ q => r
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(d) Overheating economy is a synonym for rise in excess demand.
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Atomic Propositions:
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Overheating economy
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Rise in excess demand
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Connectives:
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is a synonym for
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Formula: p <=> q
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(e) Inflation either rises or does not.
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Atomic Propositions:
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Inflation rises
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Inflation does not rise
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Connectives:
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either / or
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Formula: p
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1. Remove as many brackets as possible from the following propositions without altering their meaning (i.e. the truth table).
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(a) ((q ⇔((¬r) ∨(s ∧p))) ⇔(q ⇒p))
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(b) (((p ∧(¬q)) ∧r) ∨s)
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(c) ((p ⇒(q ∨r)) ∧(¬(r ⇒s)))
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(d) ((¬(¬(¬(q ∨r)))) ⇔(q ⇔r))
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(e) (p ∨(q ∨r))
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1. Decide using truth tables whether each of the following is a tautology, contradiction or contingency.
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(a) p ⇒¬p
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(b) p ∧q ⇒p
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(c) (p ⇒¬p) ∧(¬p ⇒p)
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