Cartesian Product of Sets

The video tutorial explains the concept of Cartesian product using a practical example of pairing shirts and pants. It defines Cartesian product as a set of ordered pairs and explores its properties, such as being a binary operation and not commutative. The tutorial also covers special cases like empty and infinite sets, and relates the Cartesian product to geometry, specifically the Cartesian plane. Finally, it discusses how to calculate the number of elements in a product set.

How many different outfits can be made with 4 shirts and 3 pants?

• 12

• 7

• 4

• 3

What is the Cartesian product of two sets?

• A set of all possible sums of elements

• A set of all possible ordered pairs

• A set of all possible differences of elements

• A set of all possible products of elements

How is the Cartesian product related to a deck of cards?

• It forms the suits of the cards

• It forms the ranks of the cards

• It forms the entire deck by combining ranks and suits

• It forms the colors of the cards

Which of the following is true about the Cartesian product?

• It is commutative

• It is a binary operation

• It is associative

• It is a unary operation

What happens to the Cartesian product if one of the sets is empty?

• It results in a set with two elements

• It results in an infinite set

• It results in a null set

• It results in a set with one element

Why is the Cartesian product named so?

• After the Cartesian plane

• After the Cartesian circle

• After the Cartesian triangle

• After the Cartesian line

What is the result of the Cartesian product of a set with itself?

• A set of single elements

• A set of unordered pairs

• A set of triplets

• A set of ordered pairs

What is the Cartesian product of three sets called?

• Ordered quadruplets

• Ordered quintuplets

• Ordered triplets

• Ordered pairs

If set A has 3 elements and set B has 4 elements, how many elements are in A cross B?

• 12

• 10

• 7

• 15

What is the significance of the order in a Cartesian product?

• Order is not important

• Order is important only in one set

• Order is important in both sets

• Order is important only in the second set