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Lesson 3 Menu Warm-up Problems. Lesson 3 MI/Vocab conditional statement if-then statement hypothesis conclusion related conditionals converse Analyze.

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Presentation on theme: "Lesson 3 Menu Warm-up Problems. Lesson 3 MI/Vocab conditional statement if-then statement hypothesis conclusion related conditionals converse Analyze."— Presentation transcript:

1 Lesson 3 Menu Warm-up Problems

2 Lesson 3 MI/Vocab conditional statement if-then statement hypothesis conclusion related conditionals converse Analyze statements in if-then form. Write the converse, inverse, and contrapositive of if-then statements. inverse contrapositive logically equivalent

3 Lesson 3 KC1

4 Lesson 3 Ex1 Identify Hypothesis and Conclusion A. Identify the hypothesis and conclusion of the following statement. Answer:Hypothesis: a polygon has 6 sides Conclusion: it is a hexagon If a polygon has 6 sides, then it is a hexagon. hypothesis conclusion

5 Lesson 3 Ex1 Identify Hypothesis and Conclusion B. Identify the hypothesis and conclusion of the following statement. Tamika will advance to the next level of play if she completes the maze in her computer game. Answer:Hypothesis: Tamika completes the maze in her computer game Conclusion: she will advance to the next level of play

6 A.A B.B C.C D.D Lesson 3 CYP1 A.Hypothesis: you will cry Conclusion: you are a baby B.Hypothesis: you are a baby Conclusion: you will cry C.Hypothesis: babies cry Conclusion: you are a baby D.none of the above A. Which of the choices correctly identifies the hypothesis and conclusion of the given conditional? If you are a baby, then you will cry.

7 Lesson 3 Ex2 Write a Conditional in If-Then Form A. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. Distance is positive. Answer:Hypothesis: a distance is measured Conclusion: it is positive If a distance is measured, then it is positive. Sometimes you must add information to a statement. Here you know that distance is measured or determined.

8 Lesson 3 Ex2 Write a Conditional in If-Then Form B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form. A five-sided polygon is a pentagon. Answer:Hypothesis: a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

9 Lesson 3 CYP2 1.A 2.B 3.C 4.D A.If an octagon has 8 sides, then it is a polygon. B.If a polygon has 8 sides, then it is an octagon. C.If a polygon is an octagon, then it has 8 sides. D.none of the above A. Which of the following is the correct if-then form of the given statement? A polygon with 8 sides is an octagon.

10 Lesson 3 Ex3 A. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:Since the result is not what was expected, the conditional statement is false. Truth Values of Conditionals The hypothesis is true, but the conclusion is false. Yukon rests for 10 days, and he still has a hurt ankle.

11 Lesson 3 Ex3 B. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:In this case, we cannot say that the statement is false. Thus, the statement is true. Truth Values of Conditionals The hypothesis is false, and the conclusion is false. The statement does not say what happens if Yukon only rests for 3 days. His ankle could possibly still heal. Yukon rests for 3 days, and he still has a hurt ankle.

12 Lesson 3 Ex3 C. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:Since what was stated is true, the conditional statement is true. Truth Values of Conditionals The hypothesis is true since Yukon rested for 10 days, and the conclusion is true because he does not have a hurt ankle. Yukon rests for 10 days, and he does not have a hurt ankle anymore.

13 Lesson 3 Ex3 D. Determine the truth value of the following statement for each set of conditions. If Yukon rests for 10 days, his ankle will heal. Answer:In this case, we cannot say that the statement is false. Thus, the statement is true. Truth Values of Conditionals The hypothesis is false, and the conclusion is true. The statement does not say what happens if Yukon only rests for 7 days. Yukon rests for 7 days, and he does not have a hurt ankle anymore.

14 1.A. 2.B. Lesson 3 CYP3 A. Determine the truth value of the following statement for each set of conditions. If it rains today, then Michael will not go skiing. It does not rain today; Michael does not go skiing. A.true B.false

15 1.A. 2.B. Lesson 3 CYP3 B. Determine the truth value of the following statement for each set of conditions. If it rains today, then Michael will not go skiing. It rains today; Michael does not go skiing. A.true B.false

16 1.A. 2.B. Lesson 3 CYP3 C. Determine the truth value of the following statement for each set of conditions. If it rains today, then Michael will not go skiing. It snows today; Michael does not go skiing. A.true B.false

17 1.A. 2.B. Lesson 3 CYP3 D. Determine the truth value of the following statement for each set of conditions. If it rains today, then Michael will not go skiing. It rains today; Michael goes skiing. A.true B.false

18 Lesson 3 KC2

19 Lesson 3 Ex4 Write the converse, inverse, and contrapositive of the statement All squares are rectangles. Determine whether each statement is true or false. If a statement is false, give a counterexample. Related Conditionals Conditional:If a shape is a square, then it is a rectangle. The conditional statement is true. First, write the conditional in if-then form. Write the converse by switching the hypothesis and conclusion of the conditional. Converse:If a shape is a rectangle, then it is a square. The converse is false. A rectangle with and w = 4 is not a square.

20 Lesson 3 Ex4 Inverse:If a shape is not a square, then it is not a rectangle. The inverse is false. A 4-sided polygon with side lengths 2, 2, 4, and 4 is not a square. The contrapositive is formed by negating the hypothesis and conclusion of the converse. Contrapositive:If a shape is not a rectangle, then it is not a square. The contrapositive is true. Related Conditionals

21 A.A B.B C.C D.D Lesson 3 CYP4 A.All 4 statements are true. B.Only the conditional and contrapositive are true. C.Only the converse and inverse are true. D.All 4 statements are false. Write the converse, inverse, and contrapositive of the statement The sum of the measures of two complementary angles is 90. Which of the following correctly describes the truth values of the four statements?

22 A.A B.B C.C D.D 5Min 3-1 A.True; 12 + (–4) = 8, and a triangle has four sides. B.True; 12 + (–4)  8, and a triangle has four sides. C.False; 12 + (–4) = 8, and a triangle has four sides. D.False; 12 + (–4)  8, and a triangle has four sides. Which choice shows a compound statement for the conjunction p and r, and also states its truth value? p: 12 + (–4) = 8. r: A triangle has four sides. (over Lesson 2-2)

23 5Min 3-2 1.A 2.B 3.C 4.D A.True; a right angle measures 90 degrees, or a triangle has four sides. B.True; a right angle measures 90 degrees, or a triangle does not have four sides. C.False; a right angle does not measure 90 degrees, or a triangle has four sides. D.False; a right angle measures 90 degrees, or a triangle has four sides. Which choice shows a compound statement for the disjunction q or r, and also states its truth value? q: A right angle measures 90 degrees. r: A triangle has four sides. (over Lesson 2-2)

24 1.A 2.B 3.C 4.D 5Min 3-3 A.True; 12 + (–4) = 8, or a triangle has four sides. B.True; 12 + (–4)  8, or a triangle has four sides. C.False; 12 + (–4)  8, or a triangle does not have four sides. D.False; 12 + (–4)  8, or a triangle has four sides. Which choice shows a compound statement for the disjunction ~p or r, and also states its truth value. p: 12 + (–4) = 8. r: A triangle has four sides. (over Lesson 2-2)

25 A.A B.B C.C D.D 5Min 3-4 A.True; a right angle does not measure 90 degrees or a triangle has four sides. B.True; a right angle measures 90 degrees and a triangle does not have four sides. C.False; a right angle does not measure 90 degrees and a triangle does not have four sides. D.False; a right angle does not measure 90 degrees and a triangle has four sides. Which choice shows a compound statement for the conjunction q and ~r, and also states its truth value? q: A right angle measures 90 degrees. r: A triangle as four sides. (over Lesson 2-2)

26 5Min 3-5 1.A 2.B 3.C 4.D A.True; 12 + (–4) = 8, or a right angle measures 90 degrees. B.True; 12 + (–4)  8, or a right angle does not measure 90 degrees. C.False; 12 + (–4) = 8, or a right angle measures 90 degrees. D.False; 12 + (–4)  8, or a right angle does not measure 90 degrees. Which choice shows a compound statement for the disjunction ~p or ~q, and also states its truth values? p: 12 + (–4) = 8. q: A right angle measures 90 degrees. (over Lesson 2-2)

27 1.A 2.B 3.C 4.D 5Min 3-6 A.s or q B.s and q C.~s and ~q D.~s or q Given the following statements which compound statement is false? s: Triangles have three sides. q: 5 + 3 = 8. (over Lesson 2-2)

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