Logic Test

What is the inverse of the following statement?

"If Jeremiah goes to the dance, then he will be grounded."

• If Jeremiah does not go to the dance, he will not be grounded.

• If Jeremiah was grounded, then he went to the dance.

• If Jeremiah was not grounded, then he did not go to the dance.

• If Jeremiah does not go to the dance, he will be grounded.

Find the contrapositive of the following statement:

"If Jack plays baseball, then Jack participates in sports."

• If Jack participates in sports, then Jack plays baseball.

• If Jack does not play baseball, then Jack does not participate in sports.

• If Jack does not participate in sports, then Jack does not play baseball.

• If Jack does not play baseball, then Jack participates in sports.

Charlie's dad said, "If it is not raining, then we will go for a bike ride." Which other statement is logically equivalent?

• If we go for a bike ride, then it is not raining.

• If we don't go on a bike ride, then it is raining.

• If it is raining, then we will not go on a bike ride.

• If it is not raining, then we will not go on a bike ride.

"If it is a Friday night, Raelene will go out to a restaurant to eat dinner."

If the statement above is always true, then which of the following statements is always true?

• If Raelene goes out to a restaurant to eat dinner, then it is Friday night.

• If it is Tuesday, Raelene will not go out to a restaurant to eat dinner.

• If Raelene does not go out to a restaurant to eat dinner, then it is not Friday night.

• If it is not Friday night, Raelene will not go out to a restaurant to eat dinner.

George's mom told him he could go to the game if he cleaned his room. Because George never showed up at the game, his friends concluded that he must not have cleaned his room.

George's friends made a valid conclusion, because the conditional statement made by his mom is logically equivalent to its-

• Contrapositive

• Inverse

• Converse

• Negations

The conditional statement p → q

is logically equivalent to -

• ~ p → ~ q

• ~ q → ~ p

• q → p

• None of the above

Which of the following is a counterexample to the following statement:

"If the product of two numbers is 24, then both of the numbers are even."

• (3)(8)

• (2)(12)

• (4)(6)

• (6)(3)

Bob, Rod, Todd, Fred, Ned, and Ted are six brothers who look somewhat alike. However, each brother has his own distinguishing characteristics.

Which brother could be used as a counter-example to the statement, "If a brother wears a hat, then he also has a beard"?

• Bob

• Rod

• Todd

• Ned

"If a number is a multiple of 10, then the number is even." The statement above is true. However, its converse is not always true. Which number could be used as a counter-example to show that the converse of the statement above is sometimes false?

• 50

• 90

• 102

• 105

What is Ms. Dwight's favorite NFL team?

(Hint: think of the cheese state)

• Packers

• Brewers

• Cowboys

• Texans