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Propositional Logic Conclusions from Given Premises

Understand and express logical propositions using premises about snow, cold, and wearing coats, translate English sentences into propositional language, and learn to differentiate statements using predicate logic.

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Propositional Logic Conclusions from Given Premises

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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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