Analyze Conditional Statements Chapter 2 2 Conditional Statement

Conditional Statement �Statement contains a HYPOTHESIS and a CONCLUSION �If it is in IF-THEN

Example �If it is raining, then there are clouds in the sky. If we

Example �If it is raining, then there are clouds in the sky. After we

Rewrite the condition statement in IF-THEN form: Two angles are supplementary, if they are

Rewrite the condition statement in IF-THEN form: Example 1 All vertebrates have a backbone.

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint) All triangles have three

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint 2) 2 When x

Negation �A statement is the opposite of the original statement Statement 1: The sky

Related Conditionals �Converse �For the converse of a conditional statement, switch the hypothesis and

Related Conditionals �Conditional Statement: If it is raining, then there are clouds in the

Related Conditionals: Example �Write the conditional statement, the converse, the inverse, and the contrapositive

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the

Related Conditionals: Example �IF-THEN Form: IF you are a guitar player, THEN you are

Related Conditionals: Example Guitar players are musicians. IF-THEN Form: IF you are a guitar

Equivalent Statements �When two statements are BOTH true or false �The conditional statements and

Bioconditional Statements �Only when a conditional statement and its converse are BOTH true �We

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional Definition: If two

Bioconditional Statements: Ex. 2 �Rewrite the statement as bioconditional Conditional Statement: If Mary is

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Analyze Conditional Statements Chapter 2. 2

Conditional Statement �Statement contains a HYPOTHESIS and a CONCLUSION �If it is in IF-THEN form �Hypothesis = ‘if’ �Conclusion = ‘then’ �Example �If it is raining, then there are clouds in the sky.

Example �If it is raining, then there are clouds in the sky. If we see IF- THEN, we circle them and write if-then form

Example �If it is raining, then there are clouds in the sky. If we see IF- THEN, we circle them and write ifthen form �If it is raining, then there are clouds in the sky. After we circle if and then, we underline the Hypothesis ONCE and the Conclusion TWICE Remember: Hypothesis = if, Conclusion = then

Example �If it is raining, then there are clouds in the sky. After we circle if and then, we underline the Hypothesis ONCE and the Conclusion TWICE �If it is raining, then there are clouds in the sky.

Rewrite the condition statement in IF-THEN form: Two angles are supplementary, if they are a linear pair.

Rewrite the condition statement in IF-THEN form: Two angles are supplementary, if they are a linear pair. Now that we have found the hypothesis and conclusion, and circled if, we must rewrite it:

Rewrite the condition statement in IF-THEN form: Two angles are supplementary, if they are a linear pair. Now that we have found the hypothesis and conclusion, and circled if, we must rewrite it: If two angles are a linear pair, then they are supplementary.

Rewrite the condition statement in IF-THEN form: Example 1 All vertebrates have a backbone. Find the hypothesis and the conclusion

Rewrite the condition statement in IF-THEN form: Example 1 All vertebrates have a backbone. Now rewrite the condition statement:

Rewrite the condition statement in IF-THEN form: Example 1 All vertebrates have a backbone. Now rewrite the condition statement: If an animal is a vertebrate, then it has a backbone.

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint) All triangles have three sides. Find the hypothesis and the conclusion

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint) All triangles have three sides. Now rewrite the condition statement:

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint) All triangles have three sides. Now rewrite the condition statement: If a polygon is a triangle, then it has three sides.

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint 2) 2 When x = 2, x = 4. Find the hypothesis and the conclusion

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint 2) 2 When x = 2, x = 4. Now rewrite the condition statement:

Rewrite the condition statement in IFTHEN form: Example 2 (checkpoint 2) 2 When x = 2, x = 4. Now rewrite the condition statement: 2 If x = 2, then x = 4.

Negation �A statement is the opposite of the original statement Statement 1: The sky is blue.

Negation �A statement is the opposite of the original statement Statement 1: The sky is blue. Negation 1: The sky is not blue Statement 2: The dog is not brown.

Negation �A statement is the opposite of the original statement Statement 1: The sky is blue. Negation 1: The sky is not blue Statement 2: The dog is not brown. Negation 2: The dog is brown. Note that statement 2 is already negative, so when you negate it, it becomes positive (Neg. x Neg. = Positive)

Related Conditionals �Converse �For the converse of a conditional statement, switch the hypothesis and the conclusion �Inverse �For the inverse of a conditional statement, negate the hypothesis AND the conclusion �Contrapositive �For the contrapositive of a conditional, we first write the converse, then negate both the hypothesis and the conclusion

Related Conditionals �Conditional Statement: If it is raining, then there are clouds in the sky. �Converse: If there are clouds in the sky, then it is raining. �Inverse: If it is not raining, then there are not any clouds in the sky. �Contrapositive: If there are not any clouds in the sky, then it is not raining.

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Guitar players are musicians. IF-THEN Form: IF you are a guitar player, THEN you are a musician. True Converse: IF you are a musician, THEN you are a guitar player.

Related Conditionals: Example �IF-THEN Form: IF you are a guitar player, THEN you are a musician. True �Converse: IF you are a musician, THEN you are a guitar player. False �Inverse: IF you are not a guitar player, THEN you are not a musician. False �Contrapositive: IF you are not a musician, THEN you are not a guitar player. True

Related Conditionals: Example Guitar players are musicians. IF-THEN Form: IF you are a guitar player, THEN you are a musician. True Converse: IF you are a musician, THEN you are a guitar player. False Inverse: IF you are not a guitar player, THEN you are not a musician. False Contrapositive: IF you are not a musician, THEN you are not a guitar player. True

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Olympians are athletes. IF-THEN Form: IF you are an Olympian, THEN you are an athlete. True Converse: IF you are an athlete, THEN you are an Olympian. False Inverse:

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Olympians are athletes. IF-THEN Form: IF you are an Olympian, THEN you are an athlete. True Converse: IF you are an athlete, THEN you are an Olympian. False Inverse: IF you are not an Olympian, THEN you are not an athlete.

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Olympians are athletes. IF-THEN Form: IF you are an Olympian, THEN you are an athlete. True Converse: IF you are an athlete, THEN you are an Olympian. False Inverse: IF you are not an Olympian, THEN you are not an athlete. False Contrapositive:

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Olympians are athletes. IF-THEN Form: IF you are an Olympian, THEN you are an athlete. True Converse: IF you are an athlete, THEN you are an Olympian. False Inverse: IF you are not an Olympian, THEN you are not an athlete. False Contrapositive: IF you are not an athlete, THEN you are not an Olympian.

Related Conditionals: Example � Write the conditional statement, the converse, the inverse, and the contrapositive of the following, then decide if each statement is true or false. Olympians are athletes. IF-THEN Form: IF you are an Olympian, THEN you are an athlete. True Converse: IF you are an athlete, THEN you are an Olympian. False Inverse: IF you are not an Olympian, THEN you are not an athlete. False Contrapositive: IF you are not an athlete, THEN you are not an Olympian. True

Equivalent Statements �When two statements are BOTH true or false �The conditional statements and its contrapositive are both true or false OR �The converse and the inverse are both true or both false

Bioconditional Statements �Only when a conditional statement and its converse are BOTH true �We use “IF AND ONLY IF” �Take out the IF, and replace THEN with IF AND ONLY IF

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional Definition: If two lines intersect to form a right angle, THEN they are perpendicular. Converse:

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional Definition: If two lines intersect to form a right angle, THEN they are perpendicular. Converse: If two lines are perpendicular, THEN they intersect to form a right angle. Are both the converse and the conditional statement (definition) true or false

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional Definition: If two lines intersect to form a right angle, THEN they are perpendicular. True Converse: If two lines are perpendicular, THEN they intersect to form a right angle. True Since both the converse and the conditional statement (definition) are true, we can write them as bioconditional

Bioconditional Statements �Example Write the definition of perpendicular lines as bioconditional Definition: If two lines intersect to form a right angle, THEN they are perpendicular. True Converse: If two lines are perpendicular, THEN they intersect to form a right angle. True Bioconditional: Two lines are perpendicular IF AND ONLY IF they intersect to form a right angle.

Bioconditional Statements: Ex. 2 �Rewrite the statement as bioconditional Conditional Statement: If Mary is in theater class, THEN she will be in the fall play. Converse:

Bioconditional Statements: Ex. 2 �Rewrite the statement as bioconditional Conditional Statement: If Mary is in theater class, THEN she will be in the fall play. Converse: If Mary is in the fall play, THEN she must be taking theater class. Are these statements true or false?

Bioconditional Statements: Ex. 2 �Rewrite the statement as bioconditional Conditional Statement: If Mary is in theater class, THEN she will be in the fall play. True Converse: If Mary is in the fall play, THEN she must be taking theater class. True Bioconditional: Mary is in the fall play, IF AND ONLY IF Mary is in theater class.