STUDY GUIDE FOR REASONING TEST IN GEOMETRY

YOU MUST BE ABLE TO DO THE FOLLOWING:

  1. IDENTIFY INDUCTIVE OR DEDUCTIVE REASONING
  2. IDENTIFY SYLLOGISM OR DETACHMENT
  3. DRAW CONCLUSIONS USING SYLLOGISM OR DETACHMENT
  4. COMPLETE TRUTH TABLES
  5. IDENTIFY TRUTH VALUES FOR BICONDITIONAL STATEMENTS (EXPLAIN WHY)

SAMPLE QUESTIONS – the answers are at the end of the this document

INDUCTIVE OR DEDUCTIVE REASONING?

  1. Given a sequence: 2,4 ,6, 8, and 10, the next number in the sequence is 12.
  2. Mrs. Keener told us on the first day of school that we would have tests on Monday. Today is Monday, so we will have a test.
  3. If it is December 25th, then it is Christmas day.
  4. If Sue fell on the wet floor, then I am going to fall too.

SYLLOGISM OR DETACHMENT?

  1. If it is cold, then you need a jacket. It is cold, so you need a jacket.
  2. If you study then you will pass. Sarah passed the test.

Conjecture: Sarah must have studied.

  1. If you run, then your heart rate will increase. If your heart rate increases, then you will be tired.

Conjecture: If you run, you will be tired.

  1. If two planes intersect, then they intersect in a line. If two planes are not parallel, then they intersect.

Conjecture: If two planes are not parallel, then they intersect in a line.

DRAW A CONCLUSION USING SYLLOGISM OR DETACHMENT.

  1. If you get an A on this test, then you did well. Po got an A. conclusion?
  2. If you read a good book, then you will enjoy yourself. If you enjoy yourself, your time is well spent. Conclusion?

TRUE OR FALSE BICONDITIONAL?

  1. An angle is straight if and only if it is 180 degrees.
  2. An angle is acute if and only if it is 40 degrees.

COMPLETE THE TRUTH TABLE.

REMEMBER YOUR BASIC FACTS!

CONJUNCTIONS ARE ALWAYS FALSE EXCEPT FOR T, T. THESE ARE AND STATEMENTS. SYMBOL UPSIDE DOWN V

DISJUNCTIONS ARE ALWAYS TRUE EXCEPT FOR F, F. THESE ARE OR STATEMENTS. SYMBOL REGULAR V

CONDITIONALS ARE ALWAYS TRUE EXCEPT FOR T, F. THESE ARE IF, THEN STATEMENTS. SYMBOL SINGLE SIDED ARROW

P / Q / P V Q / (P V Q) AND P

Answers:

  1. Inductive
  2. Deductive
  3. Deductive
  4. Inductive

Remember: inductive is examples, deductive is known facts

  1. Detachment
  2. Detachment
  3. Syllogism
  4. Syllogism

Remember: detachment PQPQ and syllogism PQQR = PR (or remember detachment has 2 parts in order, and syllogism has 3)

  1. CONCLUSION: Po did well.
  2. CONCLUSION: If you read a book, then your time is well spent.

Remember: The conclusion on detachment reasoning is Q. The conclusion on syllogism is R.

  1. True, both the original and converse is true in every case.
  2. False, The converse is true in every case. The original is not true in every case. Just because we have an acute angle does not mean it has to measure 40 degrees.

P / Q / P V Q / (P V Q) AND P
T / T / T / T
F / F / F / F
T / F / T / T
F / T / T / F