Simplify the expression 8(x+3)-4x-(x+1) a. 3x+2b. 3x+4 c. 3x+23d. 3x warm-up 2

Simplify the expression 8(x+3)-4x-(x+1) a. 3x+2b. 3x+4 c. 3x+23d. 3x warm-up 2

2.1 Conditional Statements You will determine the validity of a conditional statement and its converse. You will also find counterexamples to disprove statements that are false. Pardekooper

Pardekooper Conditional Statements If-then Statement: one statement depends on the result of a condition. Example: ''If Deanna eats the last cookie, then Leon will buy more.'‘ hypothesis conclusion hypothesis conclusion 1st part, If ____ 2nd part, then ____ If, then You forgot p q

Pardekooper Converse Statements switch the hypothesis and the conclusion Example: ''If Leon buys some more cookies, then Deanna will eat the last one.'‘ conclusion hypothesis conclusion hypothesis 1st part, If ____ 2nd part, then ____ If, then You forgot q p again

Pardekooper Lets try one Conditional this had been an actual emergency the attention signal you just heard would have been followed by official information, news, or instruction hypothesis: conclusion: If t tt this had been an actual emergency, then t tt the attention signal you just heard would have been followed by official information, news, or instruction. Note: The conditional of p →q where ‘→’ means ‘implies.’

Pardekooper Lets try one Converse this had been an actual emergency the attention signal you just heard would have been followed by official information, news, or instruction hypothesis: conclusion: If t tt the attention signal you just heard would have been followed by official information, news, or instruction, then t tt this had been an actual emergency. Note: The converse of p →q is q → p. ‘→’ means ‘implies.’

Pardekooper Negation Statements the denial of a statement If a statement is true, then its negation is false. If a statement is false, then its negation is true.

Meadows&Pardekooper Negation Statements Example:. this had not been an actual emergency the attention signal you just heard would not have been followed by official information, news, or instruction hypothesis:conclusion: If this had not been an actual emergency, then the attention signal you just heard would not have been followed by official information, news, or instruction. Note: The inverse of p → q is ~p → ~q. ‘~’ means ‘not.’

this had not been an actual emergency the attention signal you just heard would not have been followed by official information, news, or instruction conclusion: hypothesis: If the attention signal you just heard would not have been followed by official information, news, or instruction, then this had not been an actual emergency. Note: The contrapositive of p → q is ~ q → ~ p. Contrapositive Statements created by negating the hypothesis and conclusion of the converse of the given conditional.

Identify the hypothesis and conclusion of each conditional. 2. If you want to be fit, then you want to get plenty of excise. 4. “If you can see the magic in a fairy tale, you can face the future,” 6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach 8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”--Georgia O’Keeffe, artist Write each statement as a conditional. {if-then} 10. 3x-7=14 implies that 3x= All obtuse angles have measure greater than 90 o. 14. Two skew lines do not lie in the same plane. Show that each conditional is false by giving a counterexample. 16. Odd integers less than 10 are prime. 18. If you play sports with a ball and bat, then you play baseball. 2.1 Assignment page even {2-32, 48-51, omit 20,22}

2.1 Assignment page even {2-32, 48-51, omit 20,22} Write the converse of each conditional. {switch the hyp with conclusion} 24. If a triangle is a right triangle, then it has a 90 0 angle. 26. If you do not work, then you do not get paid. Write the converse, then determine if the conditional and converse are true or false. 28. If a point is in the first quadrant, then its coordinates are positive. 30. If the probability that an event will occur is 1, then the event is certain to occur. 32. If two angles has a measure 90 0, then the angles are congruent. Write the words for the symbolic ststements shown. Determine the truth value of the statement. If false, provide a counterexample. p: A figure is square. q: A figure has four congruent angles. r; A figure has four congruent sides 48. p q 49.q p 50. r q 51. (q and r) p

2.1 Assignment page even {Omit 20,22 Identify the hypothesis and conclusion of each conditional. 2. If you want to be fit, then you want to get plenty of excise. 4. “If you can see the magic in a fairy tale, you can face the future,” 6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach 8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”--Georgia O’Keeffe, artist Write each statement as a conditional. {if-then} 10. If 3x-7=14, then 3x= If you have an obtuse angles, then the measure is greater than 90 o. 14. If you have two skew lines, then they do not lie in the same plane. Show that each conditional is false by giving a counterexample , 6, 8, softball

2.1 Conditional Statements Geometry Identify the hypothesis and conclusion of each conditional. 2. If you want to be fit, then you want to get plenty of excise. 4. “If you can see the magic in a fairy tale, you can face the future,” 6. “If you can accept defeat and open your pay envelope without feeling guilty, your stealing.”--George Allen, former NFL coach 8. “…if I could paint that flower in a huge scale, you could not ignore its beauty.”-- Georgia O’Keeffe, artist Write each statement as a conditional. {if-then} 10. If 3x-7=14, then 3x= If you have an obtuse angles, then the measure is greater than 90 o. 14. If you have two skew lines, then they do not lie in the same plane. Show that each conditional is false by giving a counterexample , 6, 8, softball