Question

unit test - foundations of logic a
for the given statement below, write the conditional statement( if, then).

1. a right angle has a measure of 90.

find a counterexample for each statement below.

1. if a person is an athlete, then they play soccer.

use the conditional statement \if it is january, then there is snow.\ for questions 3 - 4.

1. identify the hypothesis:
2. identify the conclusion:

write the inverse, converse, and contraposition of the conditional statement below. determine their truth value.

1. if daniel is in 11th grade, then daniel is in high school.

converse:
validity (circle one): true or false
inverse:
validity (circle one): true or false
contrapositive:
validity (circle one): true or false

Explanation:

Step1: Write conditional statement for 1

If an angle is a right - angle, then it has a measure of 90.

Step2: Find counter - example for 2

A basketball player is an athlete but may not play soccer.

Step3: Identify hypothesis for 3

It is January.

Step4: Identify conclusion for 4

There is snow.

Step5: Write converse for 5

If Daniel is in high school, then Daniel is in 11th grade. Validity: FALSE

Step6: Write inverse for 5

If Daniel is not in 11th grade, then Daniel is not in high school. Validity: FALSE

Step7: Write contrapositive for 5

If Daniel is not in high school, then Daniel is not in 11th grade. Validity: TRUE

Answer:

1. If an angle is a right - angle, then it has a measure of 90.
2. A basketball player (an athlete who doesn't play soccer).
3. It is January.
4. There is snow.
5. Converse: If Daniel is in high school, then Daniel is in 11th grade. Validity: FALSE

Inverse: If Daniel is not in 11th grade, then Daniel is not in high school. Validity: FALSE
Contrapositive: If Daniel is not in high school, then Daniel is not in 11th grade. Validity: TRUE