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Types of Conditionals Geometry

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The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd. Conditional: (p → q) If x is prime, then x is odd. Converse: (q → p) If x is odd, then x is prime.

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pqp → qp → qq → pq → p TT TF FT FF T F T T T T F T Conditional Converse

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The inverse of a conditional statement is formed by negating the hypothesis and conclusion. p: x is prime. q: x is odd. Conditional: (p → q) If x is prime, then x is odd. Inverse: (~p → ~q) If x is not prime, then x is not odd.

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pqp → qp → q~p~q~p → ~q TT TF FT FF T F T T F F T T F T F T T T F T ConditionalInverse

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The contrapositive of a conditional statement is formed by performing the inverse and converse of the conditional statement. p: x is prime. q: x is odd. Conditional: (p → q) If x is prime, then x is odd. Contrapositive: (~q → ~p) If x is not odd, then x is not prime.

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pqp → qp → q~q~p~q → ~p TT TF FT FF T F T T F T F T F F T T T F T T A conditional and its contrapositive always has the same truth value. They are said to be logically equivalent. conditionalcontrapositive

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Write the converse, the inverse and the contrapositive for each conditional statement. 1) If the figure is a square, then it has four sides. 2) If I do not set my alarm, then I’ll be late to school.

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Write the converse, the inverse and the contrapositive for each conditional statement. 1) If the figure is a square, then it has four sides. Converse: If the figure has four sides, then it is a square. Inverse: If the figure is not a square, then it does not have four sides. Contrapositive: If the figure does not have four sides, then it is not a square.

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Write the converse, the inverse and the contrapositive for each conditional statement. 2) If I do not set my alarm, then I’ll be late to school. Converse: If I am late to school, then I did not set my alarm. Inverse: If I set my alarm, then I will not be late to school. Contrapositive: If I am not late to school, then I set my alarm.

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Homework Worksheet: Types of Conditionals #1 1.06

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