The Union Train Station switching yard puts trains going to different destinations onto different ones of their three tracks. One of their rules is, "If a train is going to Rochester, then it must be on Track 2."

Imagine you work for Amtrak and it is your job to check whether any of the trains in the switching yard violate this rule.

The cards below represent four trains. Each card represents one train. One side of the card tells whether or not that is going to Rochester and the other side tells which track it is on. Which of the following cards would you definitely need to turn over to see if any of these trains violate the rule:

"If a train is going to Rochester, then it must be on Track 2."

Don't turn over any more cards than are absolutely necessary.

At the Random House book warehouse, they have certain rules for how books should be processed. One of these is, "If a box of books has paperbacks in it, then it should be marked with 'AA'."

Imagine you're a shift supervisor at the warehouse, and it is your job to check whether any of the boxes of books in the warehouse violate this rule.

The cards below represent four boxes of books. Each card represents one box. One side of the card tells whether or not that box has paperbacks in it and the other side tells whether or not it is marked with an 'AA'. Which of the following cards would you definitely need to turn over to see if any of these boxes violate the rule:

"If a box of books has paperbacks in it, then it should be marked with 'AA'."

Don't turn over any more cards than are absolutely necessary.

A friend of yours says that this rule describes how he travels in Southern California: "If I go to Los Angeles, then I travel by train."

You want to see whether this rule is true or not.

The cards below represent what your friend did on four different days. Each card represents what he did on a different day. One side of the card tells whether he went to Los Angeles and the other side tells whether he travelled by train.

Which of the following cards would you definitely need to turn over to see if what he does on any of these days violates the rule:

"If I go to Los Angeles,

then I travel by train."

Do not turn over any more cards than are absolutely necessary.

A women's magazine claimed that this was the case: "If a woman eats salads, then she drink diet sodas."

You want to see whether this rule is true or not.

The cards below represent four women. Each card represents one woman. One side of the card tells whether the woman eats salads and the other side tells whether the woman drinks diet sodas.

Which of the following cards would you definitely need to turn over to see if any of these women violate the rule:

"If a woman eats salads,

then she drinks diet sodas."

Do not turn over any more cards than are absolutely necessary.

A medical book makes the following claim: "If a person has arthritis, then he must be over 40 years old."

You want to find out whether this rule is true or not.

The cards below represent four people. Each card represents one person. One side of the card tells whether that person has arthritis and the other side tells whether that person is over 40 years old.

Which of the following cards would you definitely need to turn over to see if any of these people violate the rule:

"If a person has arthritis, then that person must be over 40 years old."

Do not turn over any more cards than are absolutely necessary.

The following rule describes the cards below: "If a card has an 'A' on one side, then it has a '3' on the other side."

Each card below has a letter on one side and a number on the other.

Which of the following cards would you definitely need to turn over to see if any of these cards violate the rule:

"If a card has an 'A' on one side, then it has a '3' on the other side."

Do not turn over any more cards than are absolutely necessary.

The U.S. Immigration Service uses the following rule to process people's documents: "If a person comes from Europe, then their documents must be stamped with a '55'."

Imagine you work for Immigration, and you are supposed to check that people's documents have been processed properly.

The cards below represent four immigrants. One side of the card tells whether that person comes from Europe and the other side tells what code their documents have been stamped with.

Which of the following cards would you definitely need to turn over to see if any of these people's documents violate the rule:

"If a person comes from Europe, then their documents must be stamped with a '55'."

Do not turn over any more cards than are absolutely necessary.