Use inductive reasoning to decide whether the statement is true or false. Make an example or a counterexample to supplement your answer.Write your answer in a piece of paper, take a picture of it and upload it here. Include your name and section. The product of an odd counting number and an even counting number is always an even counting number.

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Inductive reasoning involves making a generalization based on observed patterns. Let's apply this to the statement: "The product of an odd counting number and an even counting number is always an even counting number."

Step 1: Understand the statement An odd counting number is a number like 1, 3, 5, 7, etc., and an even counting number is a number like 2, 4, 6, 8, etc. The statement is saying that if you multiply any odd number with any even number, the result will always be an even number.

Step 2: Test the statement Let's test this with a few examples:

• 3 (odd) x 2 (even) = 6 (even)
• 5 (odd) x 4 (even) = 20 (even)
• 7 (odd) x 6 (even) = 42 (even)

Step 3: Make a generalization Based on these examples, it seems that the statement is true. Every time we multiply an odd number with an even number, the result is an even number.

Step 4: Confirm the generalization This makes sense mathematically. An even number is defined as any integer that can be divided by 2. When you multiply an even number by any other number (whether it's odd or even), the result will still be divisible by 2, and therefore even.

So, based on inductive reasoning, the statement "The product of an odd counting number and an even counting number is always an even counting number" is true.