Deductive Reasoning Techniques and Applications

What is deductive reasoning primarily based on?

• Assumptions and guesses

• Hypotheses and experiments

• Facts, rules, definitions, and properties

• Patterns and observations

Which of the following is an example of inductive reasoning?

• If an angle is a right angle, then it is 90 degrees.

• If all observed math teachers are men, then all math teachers are men.

• If you place water in a freezer, it will freeze.

• If a figure is a square, then it is a polygon.

Why is it important to be careful with inductive reasoning?

• It is always based on facts.

• It is the same as deductive reasoning.

• It can lead to incorrect conclusions if based on limited observations.

• It is always true.

What is the Law of Detachment?

• If P implies Q and P is true, then Q is true.

• If P implies Q and P is false, then Q is false.

• If P implies Q and Q is true, then P is true.

• If P implies Q and Q is false, then P is false.

Which of the following statements is an example of the Law of Syllogism?

• If you watch baseball, you like hot dogs. If you like ketchup, you like hot dogs.

• If P implies Q and Q implies R, then P implies R.

• If an angle is a right angle, then it is 90 degrees.

• If you go into a pool, you will get wet. John was pushed into a pool, so John will get wet.

What can be concluded if a student turns in a permission slip?

• The student will fail the test.

• The student will get a reward.

• The student can go on the field trip.

• The student will not go on the field trip.

Which of the following statements is valid based on the given information: 'If a figure is a square, then it is a polygon. Figure A is a square.'?

• Figure A is a triangle.

• Figure A is a circle.

• Figure A is a polygon.

• Figure A is not a polygon.

What is always true if a conditional statement is true?

• The statement is always false.

• The converse is always true.

• The inverse is always true.

• The contrapositive is always true.

What is the contrapositive of the statement 'If it rains, then the ground is wet'?

• If the ground is not wet, then it does not rain.

• If it rains, then the ground is not wet.

• If it does not rain, then the ground is not wet.

• If the ground is wet, then it rains.

What is the result of combining the statements 'H implies M' and 'M implies B'?

• H implies B

• B implies H

• H implies M

• M implies H