Inductive reasoning means you have to find a pattern. Deductive reasoning requires you to prove it generally.
Conjecture: The difference of two even integers is always even. Deductive reasoning: See solution.
Practice makes perfect
Let's attempt to find a pattern by calculating the difference of two even integers.
2-4&=- 2 && 8-4=4
12-2&=10 &&20-14=6
Examining the differences, we see that all of them are even. With this information we can make a conjecture by inductive reasoning.
Conjecture: & The difference of two even
&integers is always even.
To use deductive reasoning, we have to prove this is true for all even integers. An even integer is defined as being divisible by 2. Therefore, we can call two arbitrary even integers 2a and 2b. Now we can write the difference of two arbitrary even integers.
2a-2b
Let's rewrite this sum and see what happens.
