Geometry (H) Worksheet: Deductive Reasoning

49 downloads 2389 Views 21KB Size Report
Geometry (H). Worksheet: Deductive Reasoning. 1. Which statement is the inverse of "If it rains, then I do not go fishing"? (A) If it does not rain, then I go fishing.
WorksheetDeductiveReasoning.nb

Geometry (H) Worksheet: Deductive Reasoning 1. Which statement is the inverse of "If it rains, then I do not go fishing"? (A) If it does not rain, then I go fishing. (B) If I do not go fishing, then it rains. (C) If it rains, then I go fishing. (D) If I go fishing, then it does not rain. 2. Given the true statements: "If the winds are above 20 knots, I will not go sailing," and "I am sailing." Which conclusion must be true? (A) The winds are increasing in intensity. (B) The winds are above 20 knots. (C) The winds are not above 20 knots. (D) The winds are decreasing in intensity. Questions 3-8 refer to the following: Given the hypothesis, duduce a conclusion. 3. Hypothesis: All students in high school are between 13 and 19 years old. Larry is a high school student. Conclusion:

4. Hypothsis: If Jeff is not in the yard, then he is watching television. Jeff is not in the

1

WorksheetDeductiveReasoning.nb

2

yard. Conclusion:

5. Hypothesis: People who make mistakes are careless. John is never careless. Conclusion:

6. Hypothesis: All moots are zoots. Booboo is a moot.

Conclusion:

7. Hypothesis: A scalene triangle has no congruent sides. DABC is scalene. Conclusion:

8. Hypothesis: In an isosceles triangle, the base angles are congruent. Conclusion:

9. Which is the contrapositive of ~p ö q? (A) ~q ö p

(B) q ö ~p

(C) ~p õ q

(D) p ö ~q

10. Which statement is the converse of the statement, "If Amanda got a ticket, then

WorksheetDeductiveReasoning.nb

3

Amanda was speeding"? (A) If amanda did not get a ticket, then Amanda was not speeding. (B) If Amanda was not speeding, then Amanda did not get a ticket. (C) If Amanda was speeding, then Amanda got a ticket. (D) If Amanda got a ticket, then Amanda was not speeding. 11. Which statement is the converse of a ö b? (A) a ö ~b

(B) b ö a

(C) ~b ö ~a

(D) ~a ö ~b

Questions 12 and 13 refer to the following. Write the converse, inverse, and contrapositive of each statement, and then determine whether each statement is true or false. 12. If Abby lives in Los Angeles, then she lives in California.

13. If two angles are right angles, then they are congruent.

WorksheetDeductiveReasoning.nb

4

14. State the five parts of a proof in two-column form. 1) 2) 3) 4) 5) 15. Given the true statements: "All tigers are animals," and "Max is not a tiger." It follows that (A) Max is an animal

(B) Max is a cat.

(C) No conclusion can be reached.

(D) Max is not an animal.

16. What is the contrapositive of the statement q ö ~p?

WorksheetDeductiveReasoning.nb

5

(A) ~p ö q

(B) p ö ~q

(C) ~p ö ~q

(D) ~q ö p

17. What is the converse of the statement "If x is even, then x + 1 is odd"? (A) If x is not even, then x + 1 is odd. (B) If x is odd, then x + 1 is even. (C) If x + 1 is odd, then x is even. (D) If y is even, then y + 1 is odd.