Tag: cartesian product of sets

Quizzes (0) Questions (74)

Questions Related to cartesian product of sets

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