Math 310-01/02

10-18-2017

1. Show by specific counterexample that the following statements are
*false*.

(a) " for all ."

(b) "The square of a real number is greater than or equal to the original number."

(c) "If m and n are integers and 6 divides , then either 6 divides m or 6 divides n."

(d) "The derivative of a product of two functions is equal to the product of the derivatives of the two functions."

(a) If , , while . Therefore, the result is false.

(b) If , then , but is not greater than or equal to . Therefore, the result is false.

(c) If and , then 6 divides , but 6 does not divide either or . Therefore, the result is false.

(d) Let and . Then

Therefore, the result is false.

*He who walks in another's tracks leaves no footprints.* -
*Joan Brannon*

Copyright 2017 by Bruce Ikenaga