Conditional Statements

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Conditional Statements

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Presentation transcript:

Conditional Statements Lesson 2.2 Conditional Statements

Conditional Statement A conditional statement is _______________ _____________________________________ Definition: ____ your feet smell and your nose runs, _______ you're built upside down. Example:

Conditional Statement - continued Conditional Statements have ______ parts: The hypothesis is the part of a conditional statement that follows _______ (when written in if-then form.) The hypothesis is _________________________________. The conclusion is the part of an if-then statement that follows ________ (when written in if-then form.) The conclusion is ______________________________.

Writing Conditional Statements Conditional statements can be written in ________form to emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the _________ into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: ____________________________________________. Example 2: Seals swim. can be written as... Conditional Statement: ____________________________________________.

Two angles are vertical __________they are congruent. If …Then vs. Implies Another way of writing an if-then statement is using the word _______________. If two angles are vertical, then they are congruent. Two angles are vertical __________they are congruent.

Conditional Statements can be true or false: A conditional statement is FALSE only when ________________ ____________________________________________________. A counterexample is an example used to show that a statement is _______________________________________________________. Statement: If you live in Virginia, then you live in Richmond. Is there a counterexample? ____________ Counterexample: ________________________________________. Therefore () the statement is _________.

Symbolic Logic Symbols can be used to ________________________________. Symbols for Hypothesis and Conclusion: Hypothesis is represented by “____”. Conclusion is represented by “____”. if ____, then _____ or ____ implies ____

Symbolic Logic - continued _______________ or _______________ ________ is used to represent Example: p: a number is prime q: a number has exactly two divisors pq: ______________________________________________

is used to represent the word Symbolic Logic - continued ____ is used to represent the word “______” Example 1: p: the angle is obtuse ~p: _____________________________________ Note: ~p means that the angle could be acute, right, or straight. Example 2: p: I am not happy ~p: _________________________________________ ~p took the “not” out; it would have been a double negative (not not)

is used to represent the word Symbolic Logic - continued _______ is used to represent the word “_______” Example: p: a number is even q: a number is divisible by 3 pq: ________________________________________. i.e. _________________________________

is used to represent the word Symbolic Logic- continued ________ “_____” is used to represent the word Example: p: a number is even q: a number is divisible by 3 pq: _______________________________________. i.e. __________________________________

is used to represent the word Symbolic Logic - continued _______ is used to represent the word “____________” Example: Therefore, the statement is false. _______________________________

Forms of Conditional Statements Converse: _____________the hypothesis and conclusion (p  q becomes ____________) Conditional: pq If two angles are vertical, then they are congruent. Converse: _______ ________________________________________.

Forms of Conditional Statements Inverse: State the __________ (or _____________) of both the hypothesis and conclusion. (p  q becomes __________) Conditional: pq : If two angles are vertical, then they are congruent. Inverse: ______ _____________________________________.

Forms of Conditional Statements Contrapositive: __________the hypothesis and conclusion and state the ____________. (p  q becomes ____________) Conditional: pq : If two angles are vertical, then they are congruent. Contrapositive: _______ ___________________________________.

Forms of Conditional Statements Contrapositives are _____________________________ _____________________________________________ If pq is true, then qp is _______. If pq is false, then qp is _______.

Biconditional When a conditional statement and its converse are both true, ____ _____________________________________________________. Use the phrase ________________ (sometimes abbreviated: ____) Statement: If an angle is right then it has a measure of 90. Converse: If an angle measures 90, then it is a right angle. Biconditional: ___________________________________________.