Inductive reasoning means you have to find a pattern. Deductive reasoning requires you to prove it generally.
Conjecture: The sum of two negative integers is always negative. Deductive reasoning: See solution.
Practice makes perfect
Let's attempt to find a pattern by calculating the sum of two negative integers.
- 1+(- 4)&=- 5 && - 5+(- 7)=- 12
- 3+(- 3)&=- 6 &&- 9+(- 11)=- 20
Examining the sums, we see that all of them are negative. With this information we can make a conjecture by inductive reasoning.
Conjecture: & The sum of two negative
&integers is always negative.
To use deductive reasoning, we have to prove this is true for all integers. If we call our arbitrary negative integers - a and - b where a>0 and b>0, we can write the sum of two arbitrary negative numbers.
- a+(- b)
Let's simplify this sum and see what happens.
