Consider the following statement. If the decimal expansion of r is terminating, then r is rational....

 

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Consider the following statement. If the decimal expansion of r is terminating, then r is rational. In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) (a) Negation The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (b) Contrapositive The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (c) Converse The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (d) Inverse The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. Consider the following statement. If the decimal expansion of r is terminating, then r is rational. In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) (a) Negation The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (b) Contrapositive The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (c) Converse The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating. (d) Inverse The decimal expansion of r is terminating and r is not rational. If the decimal expansion of r is not terminating, then r is rational. If the decimal expansion of r is not terminating, then r is not rational. If r is rational, then the decimal expansion of r is terminating. If r is not rational, then the decimal expansion of r is not terminating.

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a Negation The decimal expansion of r is not terminating or r i... View the full answer