Maths-

General

Easy

Question

# Make and test a conjecture about the sum of two even numbers.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

## The correct answer is: Hence, we conclude that the sum of two even numbers is also even and we have proved this conjecture by deductive reasoning.

### Let’s create a conjecture for the pairs (2,2), (4,6) and (8, 10). We are asked to make a conjecture about the sum of two even numbers.

So first, do the sum of even numbers in assumed pairs. We got

2 + 2 = 4

4 + 6 = 10

8 + 10 = 18

So, we conclude that the sum of two even numbers is also even and this is the conjecture.

Now, let’s see if the conjecture is true or not by deductive reasoning. Let’s say the even numbers are x and y. This even can be written as

x = 2k and y = 2l (where k and l are some integers)

Now, adding x and y

x + y = 2k + 2l

= 2(k+l)

2(k+l) is an even number

Final Answer:

Hence, we conclude that the sum of two even numbers is also even and we have proved this conjecture by deductive reasoning.

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