Fall 2021 ACP Review #1

What is the converse to this?

• If you can see a rainbow, then it is raining and sunny

• If you cannot see a rainbow, then it is not raining and sunny.

• If it is not raining and sunny, then you cannot see a rainbow.

• It is raining and sunny if and only if you can see a rainbow.

Which is the converse of the statement?

• If you are not a guitar player, then you are not a musician.

• If you are a musician, then you are a guitar player.

• You are a guitar player if and only if you are a musician.

• If you are not a musician, then you are not a guitar player.

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.

• I am hungry if and only if I eat.

Given the conditional: 

"If $2x+5=13$ , then  $x=4$ "   
Which is the inverse?

• "If  $x\ne4$ , then  $2x+5\ne13$ " 

• "If  $x=4$ , then  $2x+5=13$ " 

• "If $2x+5\ne13$ , then  $x\ne4$ "   

• " $2x+5=13$  if and only if  $x=4$ " 

What is the contrapositive to this?

• If an angle is not greater than 90, then it is not obtuse

• If an angle is not obtuse then it is not greater than 90.

• If an angle is obtuse, then it is greater than 90.

• An angle is greater than 90 if and only if it is obtuse.

What is the contrapositive to this?

• If the food is not cooked, then it is not in the oven.

• If the food is not in the oven, then it is not cooked.

• If the food is cooked, then its in the oven.

• Food is in the oven if and only if it will be cooked.

Given the conditional;

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

Which of the following is logically equivalent?

• Jose eats fish if and only if he has an allergic reaction.

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

What is logically equivalent?

• If Ty'Shawn is not late, then we won't get a tardy.

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

• Ty'Shawn is late if and only if he will get a tardy

• If Ty'Shawn doesn't get a tardy, then he is not late.

Given the conditional;

"If it is a duck then it has a beak."

Which is the biconditional?

• If it is not a duck, then it doesn't have a beak.

• It is a duck if and only if it has a beak

• If it doesn't have a beak, then it's not a duck.

• If it has a beak, then it is a duck.

Given the conditional;

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

What is the biconditional?

• 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 our class gets a treat, then we earned ten trucks.

• Our class earns ten trucks if and only if we get a treat.