Let R = \(3,3),(6,6),(9,9),(12,12),(6,12),(3,9), (3,12),(3,6)\ be a relation on the set A = \ 3,6,9,12\. The relation is

Let R = {(3,3),(6,6),(9,9),(12,12),(6,12),(3,9), (3,... | Relation (Mathematics)

(d) : For $(3,9) \in R,(9,3) \notin R$ $\\ \therefore$ Relation is not symmetric which means our choice (a) and (b) are out of court. $\\$ We need to prove reflexivity and transitivity. $\\$ For reflexivity $a \in R,(a,a) \in R$ which is hold i.e. $R$ is reflexive. $\\$ Again, for transitivity of $(a,b) \in R,(b,c) \in R$ $\\ \Rightarrow (a,c) \in R$ which is also true in $\\R = \{(3,3),(6,6),(9,9),(12,12),(6,12)$ , $(3,9),(3,12),(3,6)\}$ .

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

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