Relations Test 35

Result

Relations Test 35

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Question 1
1 / -0

Let S be the set of all triangles in a plane and let R be a relation on S defined by $$\Delta_1S\Delta_2\Leftrightarrow \Delta_1\equiv \Delta_2$$. Then, R is?

A
Reflexive and symmetric but not transitive

B
Reflexive and transitive but not symmetric

C
Symmetric and transitive but not reflexive

D
An equivalence relation

Solution
Question 2
1 / -0

Let R be a relation on $$N\times N$$, defined by $$(a, b)$$ R $$(c, d)\Leftrightarrow a+d=b+c$$. Then, R is?

A
Reflexive and symmetric but not transitive

B
Reflexive and transitive but not symmetric

C
Symmetric and transitive but not reflexive

D
An equivalence relation

Solution
Question 3
1 / -0

Let A be the set of all points in a plane and let O be the origin. Let $$R=\{(P, Q):OP=OQ\}$$. Then, R is?

A
Reflexive and symmetric but not transitive

B
Reflexive and transitive but not symmetric

C
Symmetric and transitive but not reflexive

D
An equivalence relation

Solution
Question 4
1 / -0

Let us define a relation $$R$$ in $$R$$ as $$aRb$$ if $$a \ge b$$. Then $$R$$ is

A
an equivalence relation

B
reflexive, transitive but not symmetric

C
symmetric, transitive but

D
neither transitive nor reflexive but symmetric

Solution

Given that $$aRb$$ is $$a \ge b$$
$$\Rightarrow aRa \Rightarrow a\ge a$$ which is true
let $$aRb, a\ge b$$, theb $$b \ge a$$ which is not true $$R$$ is not symmetric.
But $$aRb$$ and $$bRc$$
$$\Rightarrow a\ge b$$ and $$b\ge c$$
$$\Rightarrow a\ge c$$
Hence, $$R$$ is transitive.
Question 5
1 / -0

If $$a$$ relation $$R$$ on the set $$\left\{1,2,3\right\}$$ be defined by $$R=\left\{(1,2)\right\}$$, then $$R$$ is

A
reflexive

B
transitive

C
symmetric

D
none of these

Solution

$$R$$ on the set $$\left\{1,2,3\right\}$$ be defined by $$R=\left\{(1,2)\right\}$$
It is clear that $$R$$ is transitive.

a homogeneous relation R over a set X is transitive if for all elements a,b,c in X , whenever R relates a to b and b to c, then R also relates a to c.
Question 6
1 / -0

If A = { a , b , c , d} and B = { p , q ,r ,s} then relation from A and B is

A
{(a ,p) , ( b, r), (c , r)}

B
{(a , p), (p, q) , (c, r) , ( s , d)}

C
{{ b , a) , (q , b ) , (c , r) }

D
{ ( c,s) , ( d , s ,) ( r, a) , ( q , b )}

Solution

Because $$ { ( a , p), ( b ,r) ( c ,r)} \subseteq A \times B $$
Question 7
1 / -0

Rule from of relation {(1 ,2) , ( 2 , 5) , (3 , 10) , ( 4 , 17), ......} in N

A
$$ {(x ,y) : x , y \in N = y = 2x + 1 } $$

B
$$ {( x , y ) : x , y \in N , y = x^{2} + 1 } $$

C
$$ {( x , y ) : x , y \in N , y = 3x - 1} $$

D
$$ {( x , y ) : x , y \in N , y = x + 3} $$

Solution
Question 8
1 / -0

A relation R in N is defined such that $$ xRy \Leftrightarrow x + 4y = 16 ,$$ then the range of R is

A
{ 1 , 2 , 4}

B
{ 1 , 3 , 4}

C
{ 1 , 2 , 3}

D
{ 2 , 3 , 4}

Solution
Question 9
1 / -0

If A = { a ,b , c} , then numbers of possible non zero relations in A is

A
$$ 511$$

B
$$ 512 $$

C
$$ 7 $$

D
$$ 8 $$

Solution
Question 10
1 / -0

Let R be the relation in the set {1, 2, 3, 4} given by:
R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.

A
R is reflexive and symmetric but not transitive

B
R is reflexive and transitive but not symmetric

C
R is symmetric and transitive but not reflexive

D
R is an equivalence relation

Solution