Let A = \ 1,2,3,4\ and R be a relation on the set A A defined by R = \((a,b),(c,d)):2a + 3b = 4c + 5d\. Then the number of elements in R is

(6) : A = \ 1,2,3,4\\\ A A = \(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3), (2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)\ R = \((a,b),(c,d)):2a + 3b = 4c + 5d\\\ On checking the elements of A A, we get \((1,4),(1,2)),((2,3),(2,1)),((3,1),(1,1)),((3,4), (2,2)),((4,2),(1,2)),((4,3),(3,1))\ will satisfy R.\\ \ Number of elements in R is 6 .

Let A = { 1,2,3,4} and R be a relation on the set A X A defined by R = {((a,b),(c,d)):2a + 3b = 4c + 5d}. Then the number of elements in R is: Relation (Mathematics)

Exam (15 $\ ^{th\ }$ April $1^{st\ }$ Shift 2023)

Mathematics

Let

A = \{ 1,2,3,4\}

and

R

be a relation on the set

A \times

A

defined by

R = \{((a,b),(c,d)):2a + 3b = 4c + 5d\}

. Then the number of elements in

R

Prev Next

Explanation

(6) :

A = \{ 1,2,3,4\}

A \times A = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3)

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

R = \{((a,b),(c,d)):2a + 3b = 4c + 5d\}

\\ On checking the elements of

A \times A

, we get

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

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

will satisfy

R

.\\

\therefore\

Number of elements in

R

is 6 .

Select an option to instantly check whether it is correct or wrong.

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

Let R be the set of real numbers. end{enumerate} Statement-1: A = {(x,y) in R X R:y - x is an integer } is an equivalence . relation on R. Statement-2: B = {(x,y) in R X R:x = alpha y for some rational number } is . an equivalence relation on R.

Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

Let R be a relation on Z X Z defined by (a,b)R(c,d) if and only if ad - bc is divisible by 5 . Then R is

Let A = { 1,2,3,4,...,10} and B = { 0,1,2,3,4}. The number of elements in the relation = {(a,b) in A X A : 2(a - b)^{2} + 3(a - b) in B} is .

The number of relations, on the set { 1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is .

Let A = { 0,3,4,6,7,8,9,10} and R be the relation defined on A such that R = {(x,y) in A X A:x - y is odd positive integer or x - y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to .

If R is the smallest equivalence relation on the set { 1,2,3,4} such that {(1,2),(1,3)} subset R, then the number of elements in R is .

Let X = { 1,2,3,4,5}. The number of different ordered pairs ( Y,Z ) that can be formed such that Y subseteq X,Z subseteq X and Y cap Z. pty is

Download Divine JEE App

Quick Links

Exam Categories

Contact Info

Divine JEE