Let be the set of real numbers. enumerate Statement-1: is an integer is an equivalence . relation on .\\ Statement-2: for some rational number \ is . an equivalence relation on ....

for Statement-1.\\ (d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct . explanation for Statement-1.\\ Solution: 38. Explanation : - is an integer - is an integer is reflexive - is an integer is an integer is symmetric - are integers As sum of two integers is an integer. Ther...

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.: Relation (Mathematics)

Let

R

be the set of real numbers. \end{enumerate} Statement-1:

A = \{(x,y) \in R \times R:y - x

is an integer

\}

is an equivalence . relation on

R

.\\ Statement-2:

B = \{(x,y) \in R \times R:x = \alpha y

for some rational number \} is . an equivalence relation on

R

Statement-1 is true, Statement-2 is false.\\

Statement-1 is false, Statement-2 is true.\\

Statement-1 is true, Statement-2 is true; Statement-2 is a correct .

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 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 .

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 .

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 Z be the set of all integers, A = { (x,y) in Z X Z:(x - 2)^{2} + y^{2} ? 4 } B = { (x,y) in Z X Z:x^{2} + y^{2} ? 4 } and C = { (x,y) in Z X Z:(x - 2)^{2} + (y - 2)^{2} ? 4 } If the total number of relations from A cap B to A cap C is 2^{p}, then the value of p is

Let a relation R on N X N be defined as: ( x_{1},y_{1} )R ( x_{2},y_{2} ) if and only if x_{1} ? x_{2} or y_{1} ? y_{2}. Consider the two statements : (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

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 Z be the set of integers. If A = { x in Z:2^{(x + 2) ( x^{2} - 5x + 6 )} = 1 } and = { x in Z : - 3 < 2x - 1 < 9}, then the . number of subsets of the set A X B is

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