Relations Test 3

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Relations Test 3

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$0$$

B
$$3$$

C
$$10$$

D
None of the above

Solution

Here, $$x$$ co-ordinate will be the first entry in ordered pair.
So, option B is correct.
Question 2
1 / -0

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

A
$$0$$

B
$$3$$

C
$$10$$

D
None of the above

Solution

$$y$$ coordinate will be second entry in ordered pair.
So, option C is correct.
Question 3
1 / -0

The first component of all ordered pairs is called

A
Range

B
Domain

C
Function

D
None of these

Solution

The first components of all order pair is called Domain.
The second components of all ordered pair is called Range.
Question 4
1 / -0

If $$a$$ and $$b$$ are two variables and $$(a, b)=(b, a)$$, then

A
$$a = 0$$

B
$$b = 0$$

C
$$a = b$$

D
$$\displaystyle a\pm b$$

Solution

$$(a, b) = (b, a)$$ only if $$a = b.$$.
So, option C is correct.
Question 5
1 / -0

Which of the ordered pair satisfies the relation $$x<y$$?

A
$$(1,2)$$

B
$$(2,1)$$

C
$$(1,1)$$

D
None of these

Solution

$$(A) (1,2)$$
$$x<y$$
$$1<2$$
True , $$x<y$$

$$(B) (2,1)$$
$$2>1$$

$$(C) (1,1)$$
$$x=y$$
Question 6
1 / -0

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

A
$$(x, y)$$

B
$$(y, y)$$

C
$$(y, x)$$

D
None of the above

Solution

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

So, option A is correct.
Question 7
1 / -0

What is general representation of ordered pair for two variables $$a$$ and $$b$$?

A
$$a, b$$

B
$$(a, b)$$

C
$$(a), b$$

D
$$a, (b)$$

Solution

An ordered pair is written in the form $$(x-$$coordinate, $$y-$$coordinate$$)$$.
Question 8
1 / -0

Ordered pairs $$(x, y)$$ and $$(-1, -1)$$ are equal if $$y = -1$$ and $$x =$$ _____

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$2$$

Solution

Given , $$(x-y)=(-1,1)$$
$$x=-1, y=-1$$
The value of $$x=-1$$.
Question 9
1 / -0

Let $$A = \left \{1, 2, 3\right \}$$. Then number of equivalence relations containing $$(1, 2)$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Total possible pair=$$\{ (1,1),(1,2),(1,2),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\} $$
Reflexive means $$(a,a)$$ should be in relation.
So,$$(1,1),(2,2),(3,3)$$ should be in relation.
Symmetric means if $$(a,b)$$ is in relation,then $$(b,a)$$ should be in relation.
So,since $$(1,2)$$ is in relation $$(2,1)$$ should also be in relation.
Transitive means if $$(a,b)$$ is in relation and $$(b,c)$$ is in relation.
So if $$(1,2)$$ is in relation and $$(2,1)$$ is in relation,then $$(1,1)$$ should be in relation.
Relative $$R1=\{ (1,2),(1,1),(2,2),(3,3),(2,1)\} $$
So,smallest relation is $$R1=\{(1,2),(2,1),(1,1),(2,2),(3,3)\}$$
If we add $$(2,3)$$ ,then we have to add $$(3,2)$$ also,as it is symmetric but as $$(1,2)\&(2,3)$$ are there,we need to add $$(1,2)$$ also,as it is transitive.
As we are adding $$(1,3)$$ we should add $$(3,1)$$ also,as it is symmetric.
Relation $$R2=\{(1,2),(2,1),(1,1),(2,2),(3,3),(2,3),(1,3),(3,1)\}$$
Hence only two possible relation are there which are equivalence.
Question 10
1 / -0

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

A
$$2$$

B
$$3$$

C
$$0$$

D
$$-3$$

Solution

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 $$-3$$.

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Re-Attempt Weekly Quiz Competition

Relations Test 3

Result

Relations Test 3

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SHARING IS CARING

Question 1

$$0$$

$$3$$

$$10$$

None of the above

Solution

Question 2

$$0$$

$$3$$

$$10$$

None of the above

Solution

Question 3

Range

Domain

Function

None of these

Solution

Question 4

$$a = 0$$

$$b = 0$$

$$a = b$$

$$\displaystyle a\pm b$$

Solution

Question 5

$$(1,2)$$

$$(2,1)$$

$$(1,1)$$

None of these

Solution

Question 6

$$(x, y)$$

$$(y, y)$$

$$(y, x)$$

None of the above

Solution

Question 7

$$a, b$$

$$(a, b)$$

$$(a), b$$

$$a, (b)$$

Solution

Question 8

$$1$$

$$-1$$

$$0$$

$$2$$

Solution

Question 9

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 10

$$2$$

$$3$$

$$0$$

$$-3$$

Solution

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