Page 186 - Math Course 2 (Book 2)

Deductive Reasoning

Determine Valid Conclusions From Two Conditionals
p: Ling wants to participate in the wrestling
competition.
Use the Law of Syllogism to determine whether a
valid conclusion can be reached from each set of
q: he will have to meet an extra three times a week statements.
to practice.
(1) If you ride a bus, then you attend school.
r: he cannot take karate lessons.
(2) If you ride a bus, then you go to work.
A. valid
By the Law of Syllogism, if p → q and q → r are true. B. not valid
Then p → r is also true.
C. cannot be determined

Statement (3) is a valid
Answer conclusion by the Law of Answer
Syllogism.
(1) If your alarm clock goes off in the morning,
then you will get out of bed.
(2) If you ride a bus, then you go to work.
Your Turn! A. valid

B. not valid
Determine Valid Conclusions C. cannot be determined

The following is a true conditional. Determine Answer
whether each conclusion is valid based on the given
information. Explain your reasoning. If a polygon is
a convex quadrilateral, then the sum of the interior Analyze Conclusions
angles is 360.

Given: m∠X + m∠N + m∠O = 360 Determine whether statement (3) follows from
Conclusion: If you connect X, N, and O with statements (1) and (2) by the Law of Detachment or
segments, the figure will be a convex quadrilateral. the Law of Syllogism. If it does, state which law was
used. If it does not, select invalid.
A. valid
B. not valid (1) If a children’s movie is playing on Saturday,
C. cannot be determined Janine will take her little sister Jill to the movie.
(2) Janine always buys Jill popcorn at the movies.
(3) If a children’s movie is playing on Saturday, Jill
Answer will get popcorn.

A. Law of Detachment
B. Law of Syllogism
C. invalid
Given: ABCD is a convex quadrilateral.
Conclusion: The sum of the interior angles of Answer
ABCD is 360.
(1) If a polygon is a triangle, then the sum of the
A. valid interior angles is 180.
B. not valid (2) Polygon GHI is a triangle.
C. cannot be determined (3) The sum of the interior angles of polygon GHI
is 180.

A. Law of Detachment
Answer
B. Law of Syllogism
C. invalid

Answer

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