Understanding Cartesian Products and Ordered Pairs

The video tutorial explains the concept of Cartesian products using sets A and B. It covers how to find the Cartesian product of A and B, A and A, and B and B, detailing the process of forming ordered pairs and calculating the number of elements in each product. The tutorial emphasizes understanding the structure of ordered pairs and the cardinality of the resulting sets.

What is the Cartesian product of two sets?

• A set of numbers

• A set of single elements

• A set of ordered pairs

• A set of unordered pairs

If set A has 2 elements and set B has 3 elements, how many elements will the Cartesian product of A and B have?

• 8

• 9

• 5

• 6

Which of the following is an ordered pair from the Cartesian product of A and B, where A = {1, 2} and B = {3, 4, 5}?

• (4, 5)

• (3, 4)

• (2, 3)

• (1, 2)

How many elements are in the Cartesian product of set A with itself, if A = {1, 2}?

• 2

• 3

• 4

• 5

Which of the following is an ordered pair from the Cartesian product of A with itself, where A = {1, 2}?

• (1, 3)

• (2, 2)

• (4, 4)

• (3, 1)

What is the formula to calculate the number of elements in the Cartesian product of a set with itself?

• n / n

• n - n

• n + n

• n * n

If set B has 3 elements, how many elements will the Cartesian product of B with itself have?

• 7

• 6

• 8

• 9

Which of the following is an ordered pair from the Cartesian product of B with itself, where B = {3, 4, 5}?

• (3, 3)

• (2, 4)

• (4, 6)

• (1, 5)

What is the term used to describe the number of elements in a Cartesian product?

• Cardinality

• Multiplicity

• Duality

• Singularity

Which operation is used to find the number of elements in the Cartesian product of two sets?

• Addition

• Subtraction

• Multiplication

• Division