G.1 Conditional Statements

Which is the inverse of the statement below?

"If it is not raining, then I will not use an umbrella."

• If I use an umbrella, then it is raining.

• If I do not use an umbrella, then it is not raining

• If it is raining, then I will use an umbrella

• If it is not raining, them I will use an umbrella

If Nate eats chips, then he uses salsa dip. If Nate uses salsa dip, then he gets indigestion.

Law of Syllogism

• Nate uses salsa dip.

• Nate gets indigestion.

• If Nate uses salsa dip, then he gets indigestion.

• If Nate eats chips, then he gets indigestion.

Answer explanation

By the Law of Syllogism, what statement follows from the following pair og true statements?

If it is raining outside, then the ground is wet.

What can be concluded using the Law of Detachment?

It is raining outside.

• The ground is wet.

• It is raining outside.

• It is not raining outside.

• The ground is not wet.

Let P be "the sum of the measures of two angles are 90 degrees," and let Q be "the two angles are complementary angles."

Write in words. P ---> Q

• If two angles are complementary angles, then the sum of their measures is 90 degrees.

• If the sum of the measures of two angles is 90 degrees, then the two angles are complementary angles.

• Two angles are complementary angles if and only if the sum of their measures is 90 degress.

• If two angles are not complementary angles, then the sum of their measure is not 90 degrees

Which is the contrapositive of the statement below?

If the measure of an angle is 90 degrees, then it is a right angle.

• IF the measure of an angle is not 90 degrees, then it is not a right angle.

• If the measure of an angle is not 90 degrees, then it is a right angle.

• if an angle is not a right angle, then its measure is not 90 degrees.

• If an angle is a right angle, then its measure is 90 degrees.

What is the inverse of the statement below?

If Joe goes fishing, then Joe needs bait.

• If he needs bait, then Joe goes fishing.

• If Joe does not go fishing, then he does not need bait.

• If he does not need bait, then Joe does not go fishing.

• If joe goes fishing, then he does not need bait.

What is the converse of this statement?

"If Cathy buys some socks, then she will buy some shoes."

• If Cathy does not buy some socks, then she will not buy some shoes.

• If Cathy does not buy some shoes, then she will not buy some socks.

• If Cathy buys some shoes, then she will buy some socks

• If Cathy does not buy some shoes, them she will buy some socks.

Which is the inverse of the statement below?

If a quadrilateral is a trapezoid, then consecutive angles are supplementary.

• If the consecutive angles are supplementary, then the quadrilateral is a trapezoid

• If the consecutive angles are not supplementary, then thethen the quadrilateral is not a trapezoid

• If a quadrilateral is not a trapezoid, then consecutive angles are not supplementary

• If a quadrilateral is not a trapezoid, then then consecutive angles are supplementary.

What is the contrapositive of the following statement?

"If Carl gets a job, then he will buy a car."

• If Carl does not get a job, then then he not will buy a car."

• If Carl buys a car, then he will get a job.

• If Carl does not buys a car, then he will not get a job.

• If Carl buys a car, then he will not get a job.

Which is the converse of the statement below?

If you do your homework, then you will be prepared for the test.

• If you are prepared for the test, then you did your homework.

• If you are not prepared for the test, then you did not do your homework.

• If you do your homework, then you will be prepared for the test.

• If you do not do your homework, then you will not be prepared for the test.