Question

1. which of the following statements are conditional statements? choose all that apply. if an angle is a right angle, then its measure is 90 degrees i do not know if that is an obtuse angle i like the super mario bros. movie i do not like broccoli if you play hockey, then you know how to ice skate 2. the following conditional is false. which of the following choices is a counterexample? if you live in indiana, then you live in fort wayne. you live in fort wayne. you live in indianapolis. you live in downtown fort wayne. you live in bloomington. 3. which of the following statements is converse to the conditional statement? if two angles sum to 180°, then they are supplementary. if two angles sum to 180°, then they are supplementary. if two angles are supplementary, then they have a sum of 180°. if two angles do not have a sum to 180°, then they are not supplementary. if two angles are not supplementary, then they do not have a sum of 180°. 4. label each sentence with its logic statement: original conditional: if it is raining, then i will bring an umbrella. if i bring an umbrella, then it is raining. if it is not raining, then i will not bring an umbrella. if i do not bring an umbrella, then it is not raining.

Explanation:

1. Conditional statements have "if...then..." structure. Only the first statement fits.
2. A counterexample for "If in Indiana, then in Fort Wayne" is living in Indiana but not Fort Wayne. Indianapolis and Bloomington are such cities.
3. Converse switches hypothesis and conclusion of the conditional.
4. Converse: Q→P; Inverse: ¬P→¬Q; Contrapositive: ¬Q→¬P.

Answer:

1. If an angle is a right angle, then its measure is 90 degrees
2. B. You live in Indianapolis, D. You live in Bloomington
3. If two angles are supplementary, then they have a sum of 180°
4. Converse; Inverse; Contrapositive