Cartesian Products Of Sets

We are asked to find the intersection of

A%20%5Ctimes%20B

and

B%20%5Ctimes%20A

. Step 1: Find

A%20%5Ctimes%20B

The Cartesian product

A%20%5Ctimes%20B

consists of all ordered pairs where the first element is from

A

and the second element is from

B

A%20%5Ctimes%20B%20%3D%20%5C%7B(1%2C%201)%2C%20(1%2C%202)%2C%20(1%2C%203)%2C%20(2%2C%201)%2C%20(2%2C%202)%2C%20(2%2C%203)%2C%20(5%2C%201)%2C%20(5%2C%202)%2C%20(5%2C%203)%2C%20(6%2C%201)%2C%20(6%2C%202)%2C%20(6%2C%203)%5C%7D

Step 2: Find

B%20%5Ctimes%20A

The Cartesian product

B%20%5Ctimes%20A

consists of all ordered pairs where the first element is from

B

and the second element is from

A

B%20%5Ctimes%20A%20%3D%20%5C%7B(1%2C%201)%2C%20(1%2C%202)%2C%20(1%2C%205)%2C%20(1%2C%206)%2C%20(2%2C%201)%2C%20(2%2C%202)%2C%20(2%2C%205)%2C%20(2%2C%206)%2C%20(3%2C%201)%2C%20(3%2C%202)%2C%20(3%2C%205)%2C%20(3%2C%206)%5C%7D

Step 3: Find the intersection The intersection

A%20%5Ctimes%20B%20%5Ccap%20B%20%5Ctimes%20A

is the set of pairs that are in both products:

A%20%5Ctimes%20B%20%5Ccap%20B%20%5Ctimes%20A%20%3D%20%5C%7B(1%2C%201)%2C%20(2%2C%201)%2C%20(3%2C%202)%2C%20(2%2C%202)%5C%7D

Thus, the correct answer is

%5C%7B(1%2C%201)%2C%20(2%2C%201)%2C%20(3%2C%202)%2C%20(2%2C%202)%5C%7D

Chapter Questions
1 MCQs