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Section 2-2: Biconditionals and Definitions

Section 2-2: Biconditionals and Definitions. 2.01 Use logic and deductive reasoning to draw conclusions and solve problems. Essential Questions. 1) How are if-then statements written and interpreted ? 2) How are Venn diagrams used to draw conclusions?. Homework Answers.

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Section 2-2: Biconditionals and Definitions

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  1. Section 2-2: Biconditionals and Definitions 2.01 Use logic and deductive reasoning to draw conclusions and solve problems.

  2. Essential Questions 1) How are if-then statements written and interpreted? 2) How are Venn diagrams used to draw conclusions?

  3. Homework Answers • P 74: 64) A 65) I 66) D 67) If Marta is too young to vote, then she is 5 years old. False • P 269-270: 42) D 43) G 44) D 45) H • Complete: Check Skills, p 75 (all)

  4. Logically equivalent The statement and its contrapositive are logically equivalent. This means that the statement and its contrapositive are both true or both false.

  5. Draw concentric circles for the Venn diagram for testing conclusions for the conditional and the contrapositive. The hypothesis of each goes in the inner circle and the conclusion goes in the outer ring. If the statement one is asked to draw a conclusion about does not coincide with a hypothesis, there is no conclusion.

  6. biconditional A statement that combines a conditional and its converse with the words “if and only if” (abbreviated iff).

  7. Examples: Worksheet Conditional Conclusions Together: 1 -9 odds You: 2 – 8 evens Worksheet: 4 Questions on Biconditionals Together: 1, 3 You : 2, 4

  8. linear pair two adjacent angles that are supplementary

  9. With a partner, complete p 78 (2 – 22 even) • Individually: Practice 2-2

  10. P 78: 2)If 2x-5=19, then x=12. True. X=12 iff 2x-5=19. 4)If |x|=3, then x=3. False since |-3|= 3. 6)If x2 = 100, then x = -10. It is false since x can also equal 10.8)If an integer is divisible by 100, then its last 2 digits are zeros. If an integer’s last 2 digits are zeros, then it is divisible by 100.10)If 2 lines are II, then they are coplanar and do not intersect. If 2 lines are coplanar and do not intersect, then they are II. 12) If x2 = 144, then x=12 or x = -12. If x = 12 or x = -12, then x2 = 144. 14)Planes are II if and only if they do not intersect. 16) not reversible 18)No; it isn’t reversible. Counter: mouse 20) No; not precise; a ray or pt. could be part of a line. 22)No; not reversible. Counter: stop sign

  11. Summarize Lesson Quiz 2-2 Homework If-Then statements, Converses Worksheet Mixed Review, p 81 (55 – 69)

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