Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

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

Let A and B be two sets such that $A\times B=\left{ \left( a,1 \right) ,\left( b,3 \right) ,\left( a,3 \right) ,\left( b,1 \right) ,\left( a,2 \right) ,\left( b,2 \right)  \right} ,$ then 

  1. $A=\left\{ 1,2,3 \right\} $ and $B=\left\{ a,b \right\} $
  2. $A=\left\{ a,b \right\} $ and$ B=\left\{ 1,2,3 \right\} $
  3. $A=\left\{ 1,2,3 \right\} $ and $B\subset \left\{ a,b \right\} $
  4. $A\subset \left\{ a,b \right\} $ and $B\subset \left\{ 1,2,3 \right\} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$A$ is the first  element in  the cartesian product $A\times B=\left{a\,,b\,,a\,,b\,,a\,,b\right}$

and $B$ is the second element in  the cartesian product $A\times B=\left{1,\,3\,,3\,,1\,,2\,,2\right}$
$\therefore$ elements of $A=\left{a,b\right}$ and $B=\left{1\,,2\,,3\right}$

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.