Let be the real line. Consider the following subsets of the plane :\\ and \\ is an integer .\\ Which one of the following is true?...

(a) : "lo be an equivalence relation the relation must be all reflexive, symmetric and transitive.\\ is\\ reflexive - for i.e., \\ symmetric - for \\ i.e. \\ transitive - for and \\ and , giving i.e. .\\ is an equivalence relation on .\\ is not reflexive for would imply \\ (impossible). Thus is not ...

Let R be the real line. Consider the following subsets of the plane X R : S = {(x,y):y = x + 1 and 0 < x < 2} T = {(x,y):x - y is an integer }. Which one of the following is true?: Relation (Mathematics)

Let

R

be the real line. Consider the following subsets of the plane

\times R

:\\

S = \{(x,y):y = x + 1

and

0 < x < 2\}

T = \{(x,y):x - y

is an integer

\}

.\\ Which one of the following is true?

T

is an equivalence relation on

R

but

S

is not\\

Neither

S

nor

T

is an equivalence relation on

R

Both

S

and

T

are equivalence relations on

R

S

is an equivalence relation on

R

but

T

is not\\

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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

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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 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

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?

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 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

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