Question

Does anyone know how to make these statements false with a counterexample? 1) The reciprocal of each natural number is a natural number. 2) The opposite of each whole number is a whole number. 3) There is no integer that has a reciprocal that is an integer.

Answer 1

1. Natural numbers are also known as "counting numbers", and are whole numbers starting at 1. A simple example set is {1, 2, 3, 4, 5}. The reciprocal of a number is 1 divided by that number. The reciprocal of 2 is 1/2; this is not a natural number. 2. The set of whole numbers includes natural numbers and zero. A simple example set is {0, 1, 2, 3, 4}. The opposite of 1 is -1; this is not a whole number. 3. The set of integers include whole numbers and their negative counterparts. A simple example set is {-2, -1, 0, 1, 2}. The reciprocal of 1 is 1, which is an integer.