Answer to Question #251671 in Discrete Mathematics for Matheca

Question

(1) Use inductive reasoning to predict the next number in each list.

(a) 1, 4, 9, 16, 25, 36, 49, ?



(b) 2, 7, à ƒ ƒ ¢ ˆ ’3, 2, à ƒ ƒ ¢ ˆ ’8, à ƒ ƒ ¢ ˆ ’3, à ƒ ƒ ¢ ˆ ’13, à ƒ ƒ ¢ ˆ ’8, à ƒ ƒ ¢ ˆ ’18, ?

(c) 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, ?



(2) Find a pair of numbers that provides a counterexample to show that the given statement is false.



(a) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even

counting number.



(b) If the product of two counting numbers is an even counting

number, then both of the counting numbers are even counting
numbers.

Answer 1

1

a) This is a sequence of squares of number. The next number is 64.

b) The next number is à ¢ ˆ ’18. They differ by 5.

c) The next number is 7/8. The difference between the numerator is 1 and the difference between the denominator is 1. Also the denominator is just the numerator plus 1.

2.

a) 3+3=6 which is even. But, 3*3=9 which is odd.

b)5*4=20 which is even. But, 5 is not an even number