# Tutorial2 Propositional logic write a conclusion for these

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Tutorial#2 Propositional logic

write a conclusion for these premises. premise 1: If it is snowing, it is cold. premise 2: If it is cold, John is wearing a coat premise 3: It is snowing

• write above premises and conclusion as propositional logic.

p: it is snowing. q: it is cold. r: John is wearing a coat. --------------premise 1: p→ q premise 2: q→ r premise 3: p conclusion: r {p→ q , q→ r , p}→ r

p T T F F q T T F F r T F T F p→ q T T F F T T q→ r T F T T r T F T F

• • • 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.

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

✤ 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)

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.

Translate the following English sentences to predicate logic ★ All cats have tails. � x[cat(x)→tail(x)] ★ Mary and Paul are siblings(Mary, Paul). ★ Jane is the mother of Mary. mother(Jane, Mary). ★ Tom is a 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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