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Tutorial#2

Tutorial#2. Propositional logic. write a conclusion for these premises. premise1:If it is snowing, it is cold. premise2: If it is cold, John is wearing a coat premise3: It is snowing. write above premises and conclusion as propositional logic. p: it is snowing. q: it is cold.

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Tutorial#2

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  1. Tutorial#2 • Propositional logic

  2. write a conclusion for these premises. • premise1:If it is snowing, it is cold.premise2: If it is cold, John is wearing a coat • premise3: It is snowing

  3. write above premises and conclusion as propositional logic.

  4. p: it is snowing. • q: it is cold. • r: John is wearing a coat. • ----------------------------premise1: p→ q • premise2: q→ r • premise3: p • conclusion: r {p→ q , q→ r , p}→ r

  5. Let p stand for the proposition “I bought a lottery ticket” and q for “I won the jackpot”. Express the following as natural English sentences:(a) ¬ p • I didn’t buy a lottery ticket.(b) p ⇒ q • if I bought a lottery ticket ,then I won the jackpot.

  6. Translate the following English sentences to propositional language • Mary isn’t sick. • Paris is the capital of France . • Bob stayed up late last night and John is football player . • Paris is the capital of France and it is raining or John is football player . • Mary is sick and it is raining implies that Bob stayed up late last night • It is raining if and only if Mary is sick • It taxes go up, the inflation will rise. • Bill will take the geology course just in case it fulfils the science requirement. • x+2=7

  7. Mary isn’t sick . ¬ q • Paris is the capital of France . p • Bob stayed up late last night and John is football player . b ∧ l • Paris is the capital of France and it is raining or John is football player • (p ∧ n) ∨ l • Mary is sick and it is raining implies that Bob stayed up late last night ((q ∧ p) → t) • It is raining if and only if Mary is sick (p ↔ q) • It taxes go up, the inflation will rise. • (t → r) • Bill will take the geology course just in case it fulfils the science requirement. • (g ↔ s) • x+2=7 (not proposition sentence)

  8. Translate the following English sentences to predicate logic • All cats have tails. • Mary and Paul are siblings. • Jane is the mother of Mary. • Tom is a cat. • Every mail message larger than one megabyte will be compressed. • Somebody in the physical class is smarter than everybody in the math class.

  9. Translate the following English sentences to predicate logic • All cats have tails. ⩝x[cat(x)→tail(x)] • Mary and Paul are siblings. siblings(Mary,Paul). • Jane is the mother of Mary. mother(Jane,Mary). • Tom is a cat. cat(Tom). • Every mail message larger than one megabyte will be compressed.⩝m[larger(m,L)→compressed(m)]. • Somebody in the physical class is smarter than everybody in the math class. • [∃x physical(x), ⩝y math(y)]→smarter(x,y).

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