16.4. Inverse, Converse, and Contrapositive http://www.ck12.org
You can be sure you are on the right path if the response is no and you can be sure you are on the wrong path if the
response is yes.
Practice
Assume each statement is true. Use the contrapositive to write another statement that is related and also true.
- All unripe fruit is bad.
- All bears like honey.
- No desserts are healthy.
- Music by Taylor Swift is good.
- Everyone who is overweight is unhealthy.
Write the inverse, converse, and contrapositive for each of the following statements. - Puppies like to play.
- If I don’t like something, then I won’t buy it.
- Everyone at the party is popular.
- You like music if you go to a concert.
- All apples have cores.
I. My pants are the only things I have that are made of jean material.
II. All the clothes you gave me are the right size.
III. None of my pants are the right size.- Write each of the above statements and its contrapositive symbolically.
- Determine the final conclusion about “the clothes from you” by stringing the statements/contrapositives together.
I. Nobody who is experienced is unsuccessful.
II. Mike is always confused.
III. No successful person is always confused.- Write each of the above statements and its contrapositive symbolically.
- Determine the final conclusion about “Mike” by stringing the statements/contrapositives together.
I. All the plates that got shipped are cracked.
II. None of the plates from your mother got shipped.
III. Plates that didn’t get shipped should not go in the trash.- Write each of the above statements and its contrapositive symbolically.
- Can you determine whether or not the “plates from your mother” should go in the trash?
You learned that declarative statements can be joined with other declarative statements using the words not, and, or,
if and then. You saw that the relationship between all but the simplest statements requires investigation in a precise
way. You formalized the definitions of the words “or” and “not”. You practiced logical reasoning through puzzles,
proofs and riddles. The focus was on metamathematical logic, the how and the why of thinking mathematically.