Download Conditional Statement

Conditional Statement
 A conditional statement has two parts, a hypothesis
and a conclusion.
 When conditional statements are written in if-then
form, the part after the “if” is the hypothesis, and the
part after the “then” is the conclusion.
 p→q
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Example 1: State the hypothesis and conclusion.
 If you are 13 years old, then you are a teenager.
 Hypothesis:
 You are 13 years old
 Conclusion:
 You are a teenager
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Geometry
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Example 1: Rewrite in the if-then form
 All mammals breathe oxygen
 If an animal is a mammal, then it breathes oxygen.
 A number divisible by 9 is also divisible by 3
 If a number is divisible by 9, then it is divisible by 3.
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Negation
 The negative of the statement
 Example: Write the negative of the statement
 A is acute
 A is not acute
 ~p represents “not p” or the negation of p
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Converse, Inverse and Contrapositive
 Converse
 The converse of a conditional is formed by switching the
hypothesis and the conclusion.
 The converse of p → q is q → p
 Inverse
 Negate the hypothesis and the conclusion
 The inverse of p → q, is ~p → ~q
 Contrapositive
 Negate the hypothesis and the conclusion of the converse
 The contrapositive of p → q, is
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Geometry
~q → ~p.
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Example
 Write the (a) inverse, (b) converse, and (c)
contrapositive of the statement.
 If two angles are vertical, then the angles are congruent.
 (a) Inverse: If 2 angles are not vertical, then they are
not congruent.
 (b) Converse: If 2 angles are congruent, then they are
vertical.
 (c) Contrapositive: If 2 angles are not congruent, then
they are not vertical.
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Equivalent Statements
 When 2 statements are both true or both false
 A conditional statement is equivalent to its contrapositive.
 The inverse and the converse of any conditional are equivalent.
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Biconditional Statement
 p if and only if q
 p iff. q
 Biconditional Statement
 It is Saturday, if and only if I am working at the restaurant.
 Conditional Statement
 If it is Saturday, then I am working at the restaurant.
 Rewrite the biconditional as conditional statement
and its converse.
 Two angles are supplementary if and only if the sum of
their measures is 180°.
 Conditional:
If two angles are supplementary, then the sum of their
measures is 180°.
 Converse:
If the sum of two angles measure 180°, then they are
supplementary.
Conditional Statement:
If it rains, then the game will be cancelled.
Write down one of the following. Move to the correct
corner: inverse, converse, or contrapositive.
If the game is cancelled, then it has rained. Converse
If it does not rain, then the game will not be cancelled.
Inverse
If the game is not cancelled, then it has not rained.
Contrapositive
Conditional Statement:
If there is snow on the ground, then flowers are not in bloom.
Write down one of the following. Move to the correct
corner: inverse, converse, or contrapositive.
If there is no snow on the ground, then flowers are in bloom.
Inverse
If flowers are not in bloom, then there is snow on the ground.
Converse
If flowers are in bloom, then there is no snow on the ground.
Contrapositive
Conditional Statement:
If two points are collinear, then they lie on the same line.
Write down one of the following. Move to the correct
corner: inverse, converse, or contrapositive.
If two points lie on the same line, then they are collinear.
Converse
If two points do not lie on the same line, then they are not
collinear.
Contrapositive
If two points are not collinear, then they do not lie on the same
line.
Inverse