List 5 examples of inductive reasoning that are always true?

Question

and 5 examples of inductive reasoning that are either true or false, and if false give the counter example

(please make them simple and short)

Answer 1

There is an ambiguity in answering this question due to the fact that mathematical terminology is inconsistent with English definitions. In mathematics, inductive logic is very much deductive reasoning. Please keep in mind that a "proof by induction" is 100% deductive and 100% valid. So.... I will assume that by "inductive reasoning" you refer to the English language meaning.

1) Five examples that are true.

a) After 2, the prime numbers are sequentially 3,5,7,11,13,.... They seem to be all odd. We conclude that after 2, all prime numbers are odd.

b) Multiplying 1*3=3, 1*5=5, 3*3=9, 3*5=15. When we multiply two odd whole numbers, the product appears to always be odd. We conclude that the product of two odd numbers is odd.

c) Adding 1+3=3, 1+5=5, 3+3=9, 3+5=15. When we add two odd whole numbers, the sum appears to always be even. We conclude that the sum of two odd numbers is even.

d) Every time we have been close to a flame, we have noticed heat. We conclude that flames are hot.

e) Every time we get hungry, we notice that after eating enough, we are no longer hungry. We conclude that eating satisfies hunger.

2) Examples that are true or false

a) Every redhead I have dated had a fiery temper. I conclude that all redheads have fiery tempers. A counter example would be a mild-mannered redhead.

b) Every person I met today spoke English. I conclude that all people speak English. A counter example would be my neighbor, who speaks Spanish.

c) The odd numbers 3,5,7 are all prime. Therefore, all odd numbers are prime. A counter example is the number 9, which is composite.

d) 1 + 2 = 3 = 2*3/2

1 + 2 + 3 = 6 = 3*4/2

1 + 2 + 3 + 4 = 10 = 4*5/2

therefore

1+2+3+4+...+n = n*(n+1)/2

This is true.

e) 0+0 = 0

0 + 0 + 0 = 0

0 + 0 + 0 + 0 = 0

I conclude that adding any number of 0's, the sum will be 0.

This is true.