2.3 Deductive Reasoning

Determine the logical conclusion given the information. Then determine whether it is based on inductive or deductive reasoning.

If Kaya makes 50 sales this month at his company, then she will receive a bonus of $1000 on her paycheck. This month Kaya completed 62 sales.

• Through inductive reasoning, Kaya will receive a $1000 bonus on her paycheck this month.

• Through deductive reasoning, Kaya will not receive a $1000 bonus on her paycheck this month.

• Through deductive reasoning, Kaya will receive a $1000 bonus on her paycheck this month.

• Through inductive reasoning, Kaya will not receive a $1000 bonus on her paycheck this month.

Determine the conclusion based on the given information. Choose the correct Venn diagram to represent the situation.

Given: If a quadrilateral is a rectangle that has 4 equal sides and angles, then is it also a square. Object A is a quadrilateral that is a rectangle with 4 equal sides and angles.

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''If two numbers are even, then their sum is even'' is a true conditional, and 8 and 24 are even numbers. Use the Law of Detachment to reach a logical conclusion.

• The sum of 8 and 24 must be even.

• If the numbers 8 and 24 are even, then their sum is 32.

• If the numbers 8 and 24 are odd, then their sum is 32.

• The sum of 8 and 24 must be odd.

Which statement follows from statements (1) and (2) by the Law of Syllogism?

(1) If an object is a square, then it is a rhombus.

(2) If an object is a rhombus, then it is an equilateral.

• An object is a rhombus.

• If an object is an equilateral, then it is a square.

• An object is a square.

• If an object is a square, then it is an equilateral.

The Law of Detachment and other laws of logic can be used to provide a system for reaching logical conclusions, called _____________.

• inductive reasoning

• deductive reasoning

• reasonable doubt

• detachment reasoning