Maria knows that 0 x 0=0, that 0 x 1=0, and that 1=0 +1.She decides that any number times 0 = 0?

Question

A. induction

B. deduction

Answer 1

This is induction, NOT deduction. Here's a proof:

Basis steps:

0 x 0 = 0
1 x 0 = 0

We assume that ( n ) x 0 = 0. We already know that this works for n = 0 and n = 1 from our basis steps. So now we want to show that it also works for n + 1

( n + 1 ) x 0 = 0

This last statement is the "inductive step."

( n + 1 ) x 0 = 0
n x 0 + 1 x 0 = 0

we know that 1 x 0 = 0 so

n x 0 = 0

which completes the proof by Induction

Summary: we know that 0 x 0 = 0 and 1 x 0 = 0. We assume that n x 0 = 0. We know that this works for n = 0 and n = 1. We then ask if it's also true for n + 1. If so, it is true for all values of n - that is, since it works for 1, it must also be true for 2, and if it's true for 2, it must also be true for 3, and so on.... Turns out that it is, so n x 0 = 0 for all n.

Answer 2

I agree that it is induction because the reason for her conclusion are several specific experiences. She is not relying on the rule as a given and then making her prediction; she is relying on her previous observations. The difference between inductive and deducative reasoning is mostly in the way the arguments are expressed. By expressing this argument differently it could be made into a deductive argument. As is, it is induction.

Answer 3

Deduction

Answer 4

Yeah.

Answer 5

Educated guess again, B.