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?

<p>A point on the plane (D)</p> 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?

<p>a_1=a'_1, a_2=a'_2, a_3=a'_3,..., a_n=a'_n (A)</p> Signup and view all the answers

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

<p>2 (D)</p> Signup and view all the answers

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

<p>A×B (B)</p> Signup and view all the answers

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

<p>The order is important (D)</p> Signup and view all the answers

What is the Cartesian product of n sets denoted by?

<p>∏_(i=1)^n▒A_i (C)</p> 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?

<p>The n-th Cartesian power of set A (B)</p> Signup and view all the answers

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

<p>The Cartesian square of A (B)</p> 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={%, $}?

<p>={(x,10,%),(x,10,$),(x,20,%),(x,20,$),(y,10,%),(y,10,$),(y,20,%),(y,20,$)} (A)</p> Signup and view all the answers

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