Let A = \ 1,2,3,4\ and R = \(1,2),(2,3),(1,4)\ be a relation on A. Let S be the equivalence relation on A such that R subset S and the number of elements in S is n. Then, the minimum value of n is .

(16) : Given A = \ 1,2,3,4\ R = \(1,2),(2,3),(1,4)\ S to be equivalence, it should be reflexive, symmetric and transitive.\ For reflexive add (1,1)(2,2),(3,3),(4,4).\ For symmetric add (2,1),(3,2),(4,1).\ For transitive (1,2),(2,3) => (1,3), so add (1,3) also add (3,1) for symmetric\ and (4,1),(1,2) => (4,2), so add (4,2) also add (2,4) for symmetric.\ Therefore S = \(1,2),(2,3),(1,4),(1,1),(2,2),(3,3),(4,4), (2,1),(3,2),(4,1),(3,1),(1,3),(2,4),(4,2),(3,4), (4,3)\\ Therefore n(S) = 16

Let A = { 1,2,3,4} and R = {(1,2),(2,3),(1,4)} be a ... | Relation (Mathematics)

(16) : Given

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

R = \{(1,2),(2,3),(1,4)\}

S

to be equivalence, it should be reflexive, symmetric and transitive.\\ For reflexive add

(1,1)(2,2),(3,3),(4,4)

.\\ For symmetric add

(2,1),(3,2),(4,1)

.\\ For transitive

(1,2),(2,3) \Rightarrow (1,3)

, so add

(1,3)

also add

(3,1)

for symmetric\\ and

(4,1),(1,2) \Rightarrow (4,2)

, so add

(4,2)

also add

(2,4)

for symmetric.\\

\therefore S = \{(1,2),(2,3),(1,4),(1,1),(2,2),(3,3),(4,4)

(2,1),(3,2),(4,1),(3,1),(1,3),(2,4),(4,2),(3,4)

(4,3)\}

\therefore\ n(S) = 16

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