Mid-Chapter Quiz
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A statement is a good definition if it is reversible.
D
If the conditional statement and its converse are true, we can say that the statement is reversible and it is a good definition. Let's examine each statement and give counterexamples if the converse of the statement is incorrect. We will start with the first statement. A: Grass is green. Let's write it as a conditional statement and converse of the conditional statement. Conditional Statement If a plant is grass, then it is green. Converse If a plant is green, then it is grass. The converse of the conditional statement is false so it is not reversible. We can give a counter example for it as the following. Counterexample Wheat can also be green. As a result, Statement A is not a good definition. We can examine rest of the statements in the same way to decide which one is a good definition.
| Statement | Conditional | Converse | Counterexample | Reversible |
|---|---|---|---|---|
| A | If a plant is grass, then it is green. | If a plant is green, then it is grass. | Wheat can also be green. | NO |
| B | If a living being is a dinosaur, then it is extinct. | If a living being is extinct, then it is a dinosaur. | Woolly Mammoth is also extinct. | NO |
| C | If a unit of measure is a pound, then it weighs less than a kilogram. | If a unit of measure weighs less than a kilogram, then it is a pound. | An ounce also weighs less than a kilogram. | NO |
| D | If a unit of measure is a yard, then it is exactly 3 ft long. | If a unit of measure is exactly 3 ft long, then it is a yard | No counterexample | YES |
Therefore, statement D is a good definition.