Question

decide if each conclusion was drawn using inductive or deductive reasoning. part 1 of 2 (a) since ( 4 \times 5 = 20 ), ( 4 \times 7 = 28 ) and ( 4 \times 8 = 32 ), whenever you multiply a whole number by 4, the result will always be even. this is an example of select reasoning. part 2 of 2 (b) for any whole number ( n ), the product ( 8n ) can be written as ( 2 \times 4n ), where ( 4n ) is a whole number. therefore, the result of multiplying any whole number by 8 is always even. this is an example of select reasoning.

Explanation:

Part (a)

Inductive reasoning uses specific examples to draw a general conclusion. Here, specific multiplications (4×5, 4×7, 4×8) are used to conclude about multiplying any whole number by 4. So it's inductive.

Deductive reasoning uses general principles or definitions (like the definition of even numbers, and algebraic manipulation here: \(8n = 2\times4n\)) to reach a conclusion about a general case. So it's deductive.

Answer:

inductive

Part (b)