Mathematical Thinking and Logic

Given the conditional statement;

"If I am hungry, then I eat."

Which of the following is the inverse?

• If I eat, then I am hungry.

• If I don't eat then I am not hungry

• If I am not hungry, then I don't eat.

• If I am not hungry, then I eat.

Given the conditional statement;

"If it is Wednesday, then Jane doesn't have baseball practice."

What is the hypothesis of this statement.

• It is Wednesday

• Jane doesn't have baseball practice

• If it is Wednesday

• Then Jane doesn't have baseball practice

Given the conditional statement;

"If Max gets good grade, then he won't be grounded"

Which of the following is the contrapositive?

• If Max isn't grounded then he gets good grades.

• If Max doesn't get good grade then he will be grounded.

• If Max gets grounded then he doesn't get good grades.

• If Max gets good grades, the he will get grounded.

Given the conditional;

"If Jose eats fish, then he has an allergic reaction"

Which of the following is the converse?

• None of these

• If Jose doesn't have an allergic reaction, then he didn't eat fish.

• If Jose doesn't eat fish, then he doesn't have an allergic reaction.

• If Jose has an allergic reaction, then he ate fish.

Given the conditional;

"If Destiny goes to work tonight, then she will make money"

What is the conclusion?

• Destiny goes to work tonight

• Destiny doesn't go to work

• She will make money

• then she will make money

Given the conditional;

"If Ty'Shawn is late then he will get a tardy"

What is the inverse?

• If Ty'Shawn is on time, then we won't get a tardy.

• If Ty'Shawn gets a tardy, then he is late.

• If Ty'Shawn is late then he won't get a tardy.

• If Ty'Shawn doesn't get a tardy, then he is on time.

Given the conditional;

"If it snows then school will be closed"

Which is the inverse?

• If school is open, then it didn't snow.

• If school is closed, then it snowed.

• If it doesn't snow, then school will be open.

• Let it Snow!

Given the conditional;

"If our class earns ten trucks, then we get a treat."

What is the contrapositive?

• If our class doesn't earn ten trucks then we don't get a treat.

• If our class doesn't get a treat, then we didn't earn ten trucks.

• If out class earns ten trucks then we don't get a treat.

• Trucks!

Which is a counterexample to the following statement?

If an angle is obtuse, then it is $125\degree$ .

•  $90\degree$  

•  $57\degree$  

•  $160\degree$  

•  $180\degree$  

To fully disprove a conjecture, one needs to find only ONE counterexample.

• True

• False