Deductive Reasoning

​2.2 Inductive and Deductive Reasoning

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Multiple Choice

By definition, a BICONDITIONAL statement is:#40

• A conditional statement with two truth values

• A TRUE conditional statement with a TRUE Converse.

• A FALSE conditional statement with a TRUE Converse.

• A TRUE conditional statement with a FALSE Converse.

Multiple Choice

What is a conjecture? #5

• A statement that has been proven true.

• An unproven statement based on observations.

• A statement that has been proven false.

• An unproven statement that is assumed false.

Multiple Choice

What is a counterexample? #4

• A specific case for which a conjecture is false.

• A specific case for which a conjecture is true.

• An example of a true statement.

• An example of the converse statement.

Multiple Choice

How would you describe this pattern's rule? #18

65, 62, 59, 56, 53, 50

• Subtract 2
• Subtract 3
• Subtract 4
• Add 3

Multiple Choice

What are the missing numbers in this pattern? 12, 15, ___, 21, ____, 27 #19

• 18,23
• 18, 24
• 17, 25
• 17, 24

Deductive Reasoning

• Deductive reasoning is defined as using given information, hypothesis or accepted general rules to reach a proven conclusion

• Makes specific conclusions from general arguments

• General arguments → specific conclusions

• Logically and realistically true

• eg. I must have 23 credits to move on to year 3. I only have 20 credits. I cannot move on to year 3

Deductive Reasoning Process

• The process of deductive reasoning involves the following steps:

• Initial Assumption

• Second Premise

• Testing

• Conclusion

Multiple Choice

What does deductive reasoning use to form its arguments? #17

• patterns

• specific cases

• observed examples

• facts, definitions, accepted properties, and laws of logic

Multiple Choice

p→q p ∴q Which law is modeled? #37

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

IF All even numbers are divisible by 2 AND 28 is even THEN 28 is divisible by 2 #16

• Inductive
• Deductive

Multiple Choice

Is the conclusion based on inductive or deductive reasoning? #9

Students at Olivia’s high school must have a B average in order to participate in sports. Olivia has a B average, so she concludes that she can participate in sports at school.

• inducutive

• deductive

Inductive Reasoning

• This is the opposite of deductive reasoning. Inductive is defined as a method of logical thinking; using observations combined with experiential information already known to be true to reach a conclusion.

• Makes broad generalizations from specific observations

• Specific argument→ general conclusions

• Logically true; may/ may not be realistically true

• eg. Conrad is a father. Conrad is bald. All fathers are bald.,.

Inductive Reasoning Process

• The process of inductive reasoning involves the following steps:

• Observation

• Theory

• Induction

Multiple Choice

The process of looking for patterns to make educated guesses about a situation. #29

• Deductive Reasoning

• Inductive Reasoning

• Conjecturing

• Counterexample

Multiple Choice

p→q q→r ∴p→r Which law is modeled? #32

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Multiple Choice

Use the Law of Syllogism to make a conclusion.  If a number is divisible by 10, then it is divisible by 2.  If a number is divisible by 2, then it is even. #38

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

Multiple Choice

Use the Law of Syllogism to make a conclusion. If the perimeter of a square is 20 ft, then the length of a side is 5 ft. If the length of a side of a square is 5 ft, then the area is 25 ft². #39

• If the side of a square is 5 ft, then the perimeter is 20 ft.
• If the perimeter of a square is 20 ft, then the area is 25 ft²
• If the area of a square is 25 ft², then the side length is 5 ft. 
• If the are of a square is 25 ft², then the perimeter is 20 ft.