Answer to Question #251666 in Discrete Mathematics for Mathica

Question

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

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

(b) 2, 7, −3, 2, −8, −3, −13, −8, −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.

(3) Use deductive reasoning to show that the following procedure always produces a number that is equal to the original number.

Procedure: Pick a number. Multiply the number by 6 and add 8.

Divide the sum by 2, subtract twice the original number,

and subtract 4.

Answer 1

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