Practice and Problem-Solving Exercises

A Practice

See Problem 1.

If possible, use the Law of Detachment to make a conclusion. If it is not possible to make a conclusion, tell why.

6. If a doctor suspects her patient has a broken bone, then she should take an X-ray. Dr. Ngemba suspects Lilly has a broken arm.
7. If a rectangle has side lengths 3 cm and 4 cm, then it has area 12  cm 2 . 12 . cm squared , .  Rectangle ABCD has area 12  cm 2 . 12 . cm squared , .
8. If three points are on the same line, then they are collinear. Points X, Y, and Z are on line m.
9. If an angle is obtuse, then it is not acute. ∠ X Y Z angle x y z  is not obtuse.
10. If a student wants to go to college, then the student must study hard. Rashid wants to go to Pennsylvania State University.

See Problem 2.

If possible, use the Law of Syllogism to make a conclusion. If it is not possible to make a conclusion, tell why.

11. Ecology If an animal is a Florida panther, then its scientific name is Puma concolor coryi.

    If an animal is a Puma concolor coryi, then it is endangered.

12. If a whole number ends in 6, then it is divisible by 2.

    If a whole number ends in 4, then it is divisible by 2.

13. If a line intersects a segment at its midpoint, then the line bisects the segment.

    If a line bisects a segment, then it divides the segment into two congruent segments.

14. If you improve your vocabulary, then you will improve your score on a standardized test.

    If you read often, then you will improve your vocabulary.

See Problem 3.

Use the Law of Detachment and the Law of Syllogism to make conclusions from the following statements. If it is not possible to make a conclusion, tell why.

15. If a mountain is the highest in Alaska, then it is the highest in the United States.

    If an Alaskan mountain is more than 20,300 ft high, then it is the highest in Alaska.

    Alaska's Mount McKinley is 20,320 ft high.

16. If you live in the Bronx, then you live in New York.

    Tracy lives in the Bronx.

    If you live in New York, then you live in the eleventh state to enter the Union.

17. If you are studying botany, then you are studying biology.

    If you are studying biology, then you are studying a science.

    Shanti is taking science this year.

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