Algebra 09 - Cartesian Products, Ordered Pairs and triples

The lecture introduces the Cartesian product, a set operation that forms ordered pairs or triples from operand sets, unlike other set operations that select elements from operand sets. The Cartesian product is visualized in 2D and 3D grids, illustrating its application in coordinate systems. The concept is generalized to N sets, forming N-tuples, with the number of elements in the Cartesian product being the product of the number of elements in each operand set. The Cartesian product is named after René Descartes, whose ideas led to the Cartesian coordinate system.

What is a key difference between Cartesian products and other set operations?

• Cartesian products do not involve any new elements.

• Cartesian products create new elements called ordered pairs.

• Cartesian products only select elements from operand sets.

• Cartesian products are the same as the union of sets.

How are ordered pairs formed in a Cartesian product of two sets?

• By selecting two elements from the same set.

• By pairing each element of one set with every element of another set.

• By selecting only identical elements from both sets.

• By combining elements randomly from both sets.

Why is the order of elements important in ordered pairs?

• Because it does not affect the Cartesian product.

• Because switching the order creates the same ordered pair.

• Because switching the order creates a different ordered pair.

• Because it only matters for identical elements.

What is formed when creating a Cartesian product of three sets?

• Ordered quadruples

• Ordered triples

• Ordered pairs

• Ordered singles

How can the position in a 3D grid of ordered triples be specified?

• By the color of the triangle only.

• By the color of the star only.

• By the color of the square only.

• By the colors of the square, triangle, and star.

What are the elements of a Cartesian product formed from N sets called?

• Ordered pairs

• Ordered triples

• N-pairs

• N-tuples

How is the number of elements in a Cartesian product calculated?

• By dividing the number of elements in each operand set.

• By adding the number of elements in each operand set.

• By multiplying the number of elements in each operand set.

• By subtracting the number of elements in each operand set.