1. | The process of using facts, rules, definitions, or properties in logical order to reach a conclusion is called | |||||

conjecturing | inductive reasoning | |||||

detachment reasoning | deductive reasoning | |||||

Hint | ||||||

2. | Which law states that if and are true conditionals, then is also true? | |||||

Law of Detachment | Law of Syllogism | |||||

Law of Deductive Reasoning | Law of Conditionals | |||||

Hint | ||||||

3. | Which statement follows from statements (1) and (2) by the Law of Detachment? (1) If a triangle is an obtuse triangle, then the measure of one of the angles is greater than 90 but less than 180. |
|||||

no valid conclusion | ||||||

Hint | ||||||

4. | Which statement follows from statements (1) and (2) by the Law of Syllogism? (1) If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180. (2) If the sum of the measures of two angles is 180, then the angles are supplementary. |
|||||

If two adjacent angles form a linear pair, then the angles are supplementary. | If two adjacent angles form a linear pair, then the sum of the measures of the angles is 180. | |||||

If two angles are supplementary, then the sum of the measures of the angles is 180. | If the sum of the measures of two angles is 180, then the angles form a linear pair. | |||||

Hint | ||||||

5. | If it is raining, then Sue and Ian will not go to the football game is a true conditional, and it is raining. Use the Law of Detachment to reach a logical conclusion. |
|||||

The football game will not be played in the rain. | Sue and Ian will go to the football game. | |||||

Ian will go to the football game if Sue goes. | Sue and Ian will not go to the football game. | |||||

Hint | ||||||