Relations Test 4

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Relations Test 4

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Weekly Quiz Competition

Question 1
1 / -0

The second component of all ordered pairs of a relation is

A
Range

B
Domain

C
mapping

D
none of these

Solution

The second components of all ordered pairs of a relation is Range.
Question 2
1 / -0

A ______ maps elements of one set to another set.

A
order

B
set

C
relation

D
function

Solution

A relation map elements of one set to another set
$$R:A\to B$$
Elements in A is mapped to elements in set B.
Question 3
1 / -0

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.

A
cartesian

B
coordinate

C
simple

D
discrete

Solution

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, $$A \times B = {(1,2), (2, 2)}$$
Question 4
1 / -0

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

A
$$1$$

B
$$2$$

C
$$-1$$

D
$$0$$

Solution

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 $$2$$.
Question 5
1 / -0

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

A
$$A \times B$$

B
$$B \times A$$

C
$$A \times A$$

D
$$B \times B$$

Solution

Cartesian product of Set $$A$$ and $$B$$ is denoted by $$A\times B$$.
Question 6
1 / -0

What is the relation for the statement "A is taller than B"?

A
is taller than

B
A is taller

C
B is taller

D
is less than

Solution

A is taller than B.
A is related to B by 'taller than'.
Question 7
1 / -0

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

A
$$0$$

B
$$-1$$

C
$$2$$

D
$$1$$

Solution

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 $$0$$.
Question 8
1 / -0

If $$A = \{1, 2, 3\}, B = \{3, 4\}$$
find (A $$\times$$ B) $$\cup$$ (B $$\times$$ A)

A
$$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$

B
$$\{(2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$

C
$$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (4, 2), (4, 3)\}$$

D
None of these

Solution

$$ (A\times B) = \left \{ (1,3),(1,4),(2,3),(2,4),(3,3),(3,4) \right \} $$
$$ (B\times A) = \left \{ (3,1),(3,2),(3,3),(4,1),(4,2),(4,3) \right \} $$
$$ \Rightarrow (A\times B)\cup (B\times A)= \left \{ (1,3),(1,4),(2,3),(2,4),(3,3),(3,4),(3,1),(3,2),(4,1),(4,2),(4,3) \right \} $$
Question 9
1 / -0

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

A
{(0, 1), (1, 0)}

B
{(0, 0), (1, 1)}

C
{(0, 1), (1, 0), (1, I)}

D
A X A

Solution

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

So, $$A\times B=A\times A$$
Hence, D is correct.
Question 10
1 / -0

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

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

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

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

D
None of these

Solution

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)}

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Re-Attempt Weekly Quiz Competition

Relations Test 4

Result

Relations Test 4

Score

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Rank

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SHARING IS CARING

Question 1

Range

Domain

mapping

none of these

Solution

Question 2

order

set

relation

function

Solution

Question 3

cartesian

coordinate

simple

discrete

Solution

Question 4

$$1$$

$$2$$

$$-1$$

$$0$$

Solution

Question 5

$$A \times B$$

$$B \times A$$

$$A \times A$$

$$B \times B$$

Solution

Question 6

is taller than

A is taller

B is taller

is less than

Solution

Question 7

$$0$$

$$-1$$

$$2$$

$$1$$

Solution

Question 8

$$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$

$$\{(2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)\}$$

$$\{(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4), (3, 1), (4, 1), (4, 2), (4, 3)\}$$

None of these

Solution

Question 9

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

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

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

A X A

Solution

Question 10

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

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

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

None of these

Solution

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