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Cartesian Product of Sets Definition

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Questions and Answers

What is the condition for two ordered pairs (a,b) and (a',b') to be equal?

a=a' and b=b' (correct)

a and a' are elements of the same set

b and b' are elements of the same set

a and a' are subsets of each other

What is the main difference between the sets {a,b} and {b,a} and the ordered pairs (a,b) and (b,a)?

The size of the sets

The number of elements

The order of elements (correct)

The type of elements

What is the term used to describe an ordered collection of n elements?

n-dimensional vector (correct)

Cartesian product

Ordered n-tuple

n-ordered pair

What is the geometric interpretation of an n-dimensional vector when n=2?

A point on the plane Signup and view all the answers

What is the condition for two n-dimensional vectors (a_1,a_2,a_3,...,a_n) and (a'_1,a'_2,a'_3,...,a'_n) to be equal?

a_1=a'_1, a_2=a'_2, a_3=a'_3,..., a_n=a'_n Signup and view all the answers

What is the minimum number of sets required to form a Cartesian product?

2 Signup and view all the answers

What is the Cartesian product of sets A and B denoted by?

A×B Signup and view all the answers

In the Cartesian product of sets, what is important about the order of elements in pairs?

The order is important Signup and view all the answers

What is the Cartesian product of n sets denoted by?

∏_(i=1)^n▒A_i Signup and view all the answers

What is the special case of the Cartesian product of sets A_1, A_2, A_3,..., A_n, when all sets are equal?

The n-th Cartesian power of set A Signup and view all the answers

What is the 2nd Cartesian power of set A also called?

The Cartesian square of A Signup and view all the answers

What is the result of the Cartesian product of sets A, B, and C, when A={x,y}, B={10,20}, and C={%, $}?

={(x,10,%),(x,10,$),(x,20,%),(x,20,$),(y,10,%),(y,10,$),(y,20,%),(y,20,$)} Signup and view all the answers