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Types of Conditionals Geometry

Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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Page 1: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

Types of Conditionals

Geometry

Page 2: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 3: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

p q p → q q → p

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Conditional Converse

Page 4: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 5: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

p q p → q ~p ~q ~p → ~q

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Conditional Inverse

Page 6: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 7: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

p q p → q ~q ~p ~q → ~p

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A conditional and its contrapositive alwayshas the same truth value.

They are said to be logically equivalent.

conditional contrapositive

Page 8: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 9: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 10: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

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.

Page 11: Types of Conditionals Geometry. The converse of a conditional statement is formed by switching the hypothesis and conclusion. p: x is prime. q: x is odd

HomeworkWorksheet:

Types of Conditionals #1

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