Tag: mathematics and statistics

Questions Related to mathematics and statistics

If $x$ and $y$ coordinate of a point is $(3, 10)$, then the $x$ co-ordinate is

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

  1. $0$

  2. $3$

  3. $10$

  4. None of the above

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Correct Option: B
Explanation:

Here, $x$ co-ordinate will be the first entry in ordered pair.

So, option B is correct.

If ordered pair $(a, b)$ is given as $(-2, 0)$, then $a =$

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

  1. $-2$

  2. $0$

  3. $2$

  4. None of the above

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Correct Option: A
Explanation:

$a$ will be first entry in ordered pair $(a, b).$

So, option A is correct.

If $y$ is second entry and $x$ is first entry then its ordered pair will be ............

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

  1. $(x, y)$

  2. $(y, y)$

  3. $(y, x)$

  4. None of the above

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Correct Option: A
Explanation:

If $x$ is first entry and $y$ is second, then its ordered pair will be $(x, y)$.


So, option A is correct.

Identify the first component of an ordered pair $(2, 1)$.

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

  1. $1$

  2. $2$

  3. $-1$

  4. $0$

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Correct Option: B
Explanation:

In an ordered pair $(x,y)$, the first component is $x$ and the second component is $y$.

Therefore, in an ordered pair $(2,1)$, the first component is $2$.

Cartesian product of sets $A$ and $B$ is denoted by _______.

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

  1. $A \times B$

  2. $B \times A$

  3. $A \times A$

  4. $B \times B$

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Correct Option: A
Explanation:

Cartesian product of Set $A$ and $B$ is denoted by $A\times B$.

Identify the first component of an ordered pair $(0, -1) $.

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

  1. $0$

  2. $-1$

  3. $2$

  4. $1$

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Correct Option: A
Explanation:

In an ordered pair $(x,y)$, the first component is $x$ and the second component is $y$.

Therefore, in an ordered pair $(0,-1)$, the first component is $0$.

Find the second component of an ordered pair $(2, -3)$

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

  1. $2$

  2. $3$

  3. $0$

  4. $-3$

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Correct Option: D
Explanation:

In an ordered pair $(x,y)$, the first component is $x$ and the second component is $y$.

Therefore, in an ordered pair $(2,-3)$, the second component is $-3$.

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.

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

  1. cartesian

  2. coordinate

  3. simple

  4. discrete

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Correct Option: A
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, $A \times B = {(1,2), (2, 2)}$

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

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

  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

Show answer
Correct Option: A
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)}

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

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

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

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

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

  4. A X A

Show answer
Correct Option: D
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.