Tag: cartesian product

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Questions Related to cartesian product

Multiple choice mathematics and statistics relations cartesian product of sets cartesian product of two sets cartesian product
State True or False
Let $A = \{1, 2\}$ and $B = \{2, 3, 4\}$, then A $\times$ B = B $\times$ A ?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.

So, $ A \times B = $ { $ (1,2), (1,3), (1,4), (2,2), (2,3), (2,4) $ }

And $ B \times A = $ { $ (2,1), (2,2), (3,1), (3,2), (4,1), (4,2) $ }

Clearly, $ A \times B \neq B \times A $

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

If $A = \left{2,3\right}$ and $B = \left{1,2\right}$, then $A \times B$ is equal to 

  1. $\left\{(2,1), (2,2), (3,1), (3,2)\right\}$
  2. $\left\{(1,2), (1,3), (2,2), (2,3)\right\}$
  3. $\left\{(2,1), (3,2)\right\}$
  4. $\left\{(1,2), (2,3)\right\}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If $A$ and $B$ are any two non-empty sets.
then $A\times B$$=\left{(x,y):x\in A  and  y\in B\right}$
As $A = \left{2,3\right}$ and $B = \left{1,2\right}$
$A \times B$$=\left{(2,1), (2,2), (3,1), (3,2)\right}$
Hence, option A.

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

If $\displaystyle A=\left{ 2,4,5 \right} ,B=\left{ 7,8,9 \right} $ then $\displaystyle n\left( A \times B \right) $ is equal to

  1. $6$
  2. $9$
  3. $3$
  4. $0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle A=\left{ 2,4,5 \right} ,B=\left{ 7,8,9 \right} $

$\Rightarrow n(A)=3$  and  $n(B)=3$

$\therefore  n(A\times B)=n(A)n(B)=9$

Hence, option B.

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

If $A=\left {1, 2,3\right }$ and $B=\left {3,8\right }$, then $(A\cup B)\times (A\cap B)$ is equal to

  1. $\left \{(8,3), (8,2), (8,1), (8,8)\right \}$
  2. $\left \{(1,2), (2,2), (3,3), (8,8)\right \}$
  3. $\left \{(3,1), (3,2), (3,3), (3,8)\right \}$
  4. $\left \{(1,3), (2,3), (3,3), (8,3)\right \}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, $A=\left {1, 2,3\right }$ and $B=\left {3,8\right }$,
Therefore, $A\cup B=\left {1,2,3\right }\cup \left {3,8\right }=\left {1,2,3,8\right }$
and $A\cap B=\left {1,2,3\right }\cap \left {3,8\right }=\left {3\right }$
$\therefore (A\cup B)\times (A\cap B)=\left {1,2,3,8\right }\times \left {3\right }$
$=\left {(1,3), (2,3), (3,3), (8,3)\right }$

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

What is the Cartesian product of $A = \left {1, 2\right }$ and $B = \left {a, b\right }$?

  1. $\left \{(1, a), (1, b), (2, a), (b, b)\right \}$
  2. $\left \{(1, 1), (2, 2), (a, a), (b, b)\right \}$
  3. $\left \{(1, a), (2, a), (1, b), (2, b)\right \}$
  4. $\left \{(1, 1), (a, a), (2, a), (1, b)\right \}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If $A $ and $B$ are two non empty sets, then the Cartesian product $A \times B$ is set of all ordered pairs $(a,b)$ such that $a\in A$ and $b\in B$.


Given $A ={1,2}$ and $B = {a,b}$

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