Tag: mathematics and statistics

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Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

The ______ product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set.

  1. cartesian

  2. coordinate

  3. simple

  4. discrete
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cartesian product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set. 
Example:$ A = {1, 2} \quad B = {2}$
cartesian product, $A \times B = {(1,2), (2, 2)}$

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

If $A = {a, b}, B={1, 2, 3}$, find B $\times$ A

  1. $B$ $\times$ $A$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b), (3, b)\}$
  2. $B$ $\times$ $A$$ = \{ (2, a), (3, a), (1, b) (2, b), (3, b)\}$
  3. $B$ $\times$ $A$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b)\}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find B × A multiply each element of B with that of A & form an ordered pair.

 i.e. ordered pairs are (1,a); (2,a); (3,a); (1,b); (2,b); (3,b)
Therefore B × A = {  (1,a), (2,a), (3,a), (1,b), (2,b), (3,b)}

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product

If A= {0, 1} and B ={1, 0}, then what is A x B equal to ?

  1. {(0, 1), (1, 0)}

  2. {(0, 0), (1, 1)}

  3. {(0, 1), (1, 0), (1, I)}

  4. A X A
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\left{ { 0,1 } \right} \times \left{ 1,0 \right} ={ \left{ (0,1),(0,0),(1,1),(1,0) \right}  }$

$\left{ { 0,1 } \right} \times \left{ 0,1 \right} ={ \left{ (0,0),(0,1),(1,0),(1,1) \right}  }$

So, $A\times B=A\times A$
Hence, D is correct.