Question

deductive reasoning
the process of arriving at a conclusion through facts and definitions
example: students at olivias high school must have a b average in order to participate in sports. olivia has a b average, so
she concludes that she can participate in sports at school
if possible, make a conclusion using deductive reasoning. if it is not possible to make a conclusion, explain why

1. if you pass a road test, you will get your drivers license.

tamara passed her road test.

1. if you swim 100 m in less than 90 s, you will be on the swim team.

jeremy swam 200 m in 190 s.

1. if you arrive at the theater by 2:00 p.m., you can see the show.

julie arrived at the theater at 1:45 p.m.

1. if a triangle has one obtuse angle, then it is an obtuse triangle.

△abc is a scalene triangle (a scalene triangle is a triangle with three different side lengths)

Explanation:

Step1: Analyze the first problem

The rule is "If you pass a road test, you will get your driver’s license." Tamara passed her road test. This satisfies the condition of the rule.

Step2: Analyze the second problem

The rule is about swimming 100m in less than 90s. Jeremy swam 200m in 190s. There is no direct relation to the 100m - 90s rule.

Step3: Analyze the third problem

The rule is "If you arrive at the theater by 2:00 P.M., you can see the show." Julie arrived at 1:45 P.M. which is earlier than 2:00 P.M. and satisfies the condition.

Step4: Analyze the fourth problem

The rule is about a triangle having an obtuse angle. $\triangle ABC$ is a scalene triangle. Scalene just refers to side lengths, not angles.

Answer:

1. Tamara will get her driver’s license.
2. No conclusion can be made as Jeremy's 200m - 190s swim has no relation to the 100m - 90s rule.
3. Julie can see the show.
4. No conclusion can be made as the given information about $\triangle ABC$ (scalene) is about side lengths, not angles (the rule is about angles).