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Lecture-03

# Lecture-03 - Lecture 3 Translating from spoken language to...

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Lecture 3: Translating from spoken language to formal notation 1. Translating five statement operators 2. Translating compound statements 3. Translating arguments Five Statement Operators: Negation Negation is expressed in a number of ways in English The cat is on the mat. The cat is not on the mat. The cat is n’t on the mat. It is false that the cat is on the mat. Five Statement Operators: Negation The cat is on the mat. = C The cat is not on the mat. The cat is n’t on the mat. It is false that the cat is on the mat. ~ C Five Statement Operators: Conjunction Roses are red. = R Violets are blue. = V Roses are red and violets are blue. Roses are red but violets are blue. Both roses are red and violets are blue. R ! V Five Statement Operators: Conjunction Roses are red. = R Apples are red. = A Roses are red and apples are red. Roses and apples are red. Both roses and apples are red. R ! A Five Statement Operators: Conjunction Apples are sweet. = S Apples are red. = A Apples are sweet and apples are red. Apples are sweet and red. Apples are both sweet and red. S ! A

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Five Statement Operators: Conjunction Components of a conjunction are conjuncts . S ! A Five Statement Operators: Disjunction Dallas will win the Superbowl. Buffalo will win the Superbowl. Dallas will win the Superbowl or Buffalo will win the Superbowl. Either Dallas will win the Superbowl or Buffalo will win the Superbowl. Five Statement Operators: Disjunction Either Dallas will win the Superbowl or Buffalo will win the Superbowl. Either Dallas or Buffalo will win the Superbowl. Dallas will win the Superbowl unless Buffalo wins the Superbowl. Five Statement Operators: Disjunction Dallas will win the Superbowl. = D Buffalo will win the Superbowl. = B Dallas will win the Superbowl or Buffalo will win the Superbowl. D v B Five Statement Operators: Disjunction Components of a disjunction are called disjuncts . D v B Five Statement Operators: Conditional You earn exactly 900 points. = N You get a some form of A. = A If you earn exactly 900 points, then you will get some form of A. N A Statement following ‘if’ is antecedent, statement following ‘then’ is consequent. (Does not apply to ‘ only if’.)
Five Statement Operators: Conditional If you earn exactly 900 points, you will get some form of A. N A Statement following ‘if’ is antecedent, statement following where the ‘then’ would be is consequent.

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