Question

Use what you know about compound statements to determine if "A piece of paper is an object that can be drawn on " would be considered a good definition. Explain.

Answer 1

The statement is a biconditional statement that can be written as a conjunction.The converse, “If an object can be drawn on, then it is a piece of paper”, is false.Both the conditional statement and its converse must be true.

Answer 2

 The statement would not be considered a good definition. The statement is a biconditional statement that can be written as the conjunction of a conditional statement and its converse. We can write it as "If an object is a piece of paper, then it can be drawn on, and if an object can be drawn on, then it is a piece of paper.” The conditional statement is true, but its converse is not. A counterexample would be that you can draw on a marker board. A good definition requires that both the conditional statement and its converse are true.