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Lesson 2-1 LESSON 2-1 CONDITIONAL STATEMENTS 1 Conditional Statements.

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Presentation on theme: "Lesson 2-1 LESSON 2-1 CONDITIONAL STATEMENTS 1 Conditional Statements."— Presentation transcript:

1 Lesson 2-1 LESSON 2-1 CONDITIONAL STATEMENTS 1 Conditional Statements

2 Conditional Statement LESSON 2-1 CONDITIONAL STATEMENTS 2 Definition:A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Example:If your feet smell and your nose runs, then you're built upside down. Continued……

3 Conditional Statement - continued Conditional Statements have two parts: LESSON 2-1 CONDITIONAL STATEMENTS 3 The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The conclusion is the part of an if-then statement that follows “then” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusion is the result of the given information.

4 Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. LESSON 2-1 CONDITIONAL STATEMENTS 4 Writing Conditional Statements Hint: Turn the subject into the hypothesis. Example 1:Vertical angles are congruent.can be written as... If two angles are vertical, then they are congruent. Conditional Statement: Example 2:Seals swim. can be written as... Conditional Statement: If an animal is a seal, then it swims.

5 Conditional Statements can be true or false: A conditional statement is false only when the hypothesis is true, but the conclusion is false. LESSON 2-1 CONDITIONAL STATEMENTS 5 A counterexample is an example used to show that a statement is not always true and therefore false. If you live in Virginia, then you live in Richmond.Statement: Counterexample:I live in Virginia, BUT I live in Coeburn. Is there a counterexample? Therefore (  ) the statement is false. Yes !!!

6 Symbolic Logic Symbols can be used to modify or connect statements. Symbols for Hypothesis and Conclusion: Hypothesis is represented by “p”. Conclusion is represented by “q”. if p, then q or p implies q LESSON 2-1 CONDITIONAL STATEMENTS 6 Continued…..

7 Symbolic Logic – Implies, if - then if p, then q or p implies q LESSON 2-1 CONDITIONAL STATEMENTS 7 is used to represent p  q Example: p: a number is prime q: a number has exactly two divisors If a number is prime, then it has exactly two divisors. p  q: Continued…..

8 If 2x – 6 =10, then x = 8. If an angle is acute, then the angles is not obtuse. LESSON 2-1 CONDITIONAL STATEMENTS 8 Underline the hypothesis and circle the conclusion for each conditional statement.

9 LESSON 2-1 CONDITIONAL STATEMENTS 9 Angles that form a linear pair are supplementary. A right angle has a measure of 90. Write each statement in if-then form.

10 is used to represent the word LESSON 2-1 CONDITIONAL STATEMENTS 10 “not” ~ Symbolic Logic - not Example 1:p: the angle is obtuse The angle is not obtuse ~p means that the angle could be acute, right, or straight. ~p: Note: Example 2:p: I am not happy ~p: I am happy ~p took the “not” out- it would have been a double negative (not not)

11 is used to represent the word LESSON 2-1 CONDITIONAL STATEMENTS 11 Symbolic Logic – Conjunction “and”  Example: p: a number is even q: a number is divisible by 3 A number is even and it is divisible by 3. i.e. 6,12,18,24,30,36,42... p  q: Conjunctions are ONLY true if both statements are true.

12 is used to represent the word LESSON 2-1 CONDITIONAL STATEMENTS 12 Symbolic Logic- Disjunction “or”  Example: p: a number is even q: a number is divisible by 3 p  q: A number is even or it is divisible by 3. i.e. 2,3,4,6,8,9,10,12,14,15,... Disjunction are ONLY false if both statements are false.

13 LESSON 2-1 CONDITIONAL STATEMENTS 13 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 ~p 1) ~p

14 LESSON 2-1 CONDITIONAL STATEMENTS 14 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 ~r 2) ~r

15 LESSON 2-1 CONDITIONAL STATEMENTS 15 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 3)

16 LESSON 2-1 CONDITIONAL STATEMENTS 16 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 4)

17 LESSON 2-1 CONDITIONAL STATEMENTS 17 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 5)

18 LESSON 2-1 CONDITIONAL STATEMENTS 18 Use the following statements to write a compound statement for each conjunction and disjunction. Then find its truth value. p: 24 hours = 1 day q: congruent supplementary angles each have a measure of 90 r: -10 + 9 < -1 6)

19 CONVERSE Converse: Switch the hypothesis and conclusion (q  p) p  q If two angles are vertical, then they are congruent. q  p If two angles are congruent, then they are vertical. LESSON 2-1 CONDITIONAL STATEMENTS 19 Continued…..

20 INVERSE Inverse: State the opposite of both the hypothesis and conclusion. (~p  ~q) p  q : If two angles are vertical, then they are congruent. ~p  ~q: If two angles are not vertical, then they are not congruent. LESSON 2-1 CONDITIONAL STATEMENTS 20

21 CONTRAPOSITIVE Contrapositive: Switch the hypothesis and conclusion and state their opposites. ( ~q  ~p) p  q : If two angles are vertical, then they are congruent. ~q  ~p: If two angles are not congruent, then they are not vertical. LESSON 2-1 CONDITIONAL STATEMENTS 21

22 LESSON 2-1 CONDITIONAL STATEMENTS 22 Write the converse, inverse and contrapositive of the conditional statement. If a number is even, then the number is four.

23 LESSON 2-1 CONDITIONAL STATEMENTS 23

24 Biconditional When a conditional statement and its converse are both true, the two statements may be combined. Use the phrase if and only if (sometimes abbreviated: iff) LESSON 2-1 CONDITIONAL STATEMENTS 24 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: An angle is right if and only if it measures 90 .

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