Inductive reasoning means you have to find a pattern. Deductive reasoning requires you to prove something generally.
The sum of a number and itself is always even. See solution.
Practice makes perfect
Let's attempt to find a pattern by calculating the sum of some numbers and themselves.
2+2&=4 &&3+3=6 [0.8em]
5+5&=10 &&6+6=12Examining the sums, we see that all of them are even. With this information we can make a conjecture by inductive reasoning.
Conjecture: & The sum of a number and
&itself is always even.
To use deductive reasoning, we have to prove this is true for all numbers. Let's call the number x.
x+x=2x
As we can see, the sum of a number and itself can be rewritten as a product where one factor is 2. The definition of an even number is that it is divisible by 2, which means our conjecture is true.
