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Each of the following defines a relation...

Each of the following defines a relation on N: `x -> y , (i) x , y in N x+y=10 x , integer, (iii) `x , y in N` `x+4y=10 ,x , y in N`

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Each of the following defines a relation on N : (i) x > y ,\ x ,\ y in N (ii) x+y=10 ,\ x ,\ y in N (iii) x y is square of an integer, x ,\ y in N (iv) x+4y=10 ,\ x ,\ y in N Determine which of the above relations are reflexive, symmetric and transitive.

Determine the domain and range of the following relations: (i) {(1,2),(1,4),(1,6),(1,8)} (ii) {(x,y), x in N, y in N and x +y=10} (iii) {(x,y): x in N, x lt 5, y =3} (iv) {(x,y): y= |x-1|, x in Z and |x| le 3}

Let N denotes the set of all natural numbers. Define two binary relations on N as: R_(1) ={(x,y) in N xx N : 2x + y = 10} R_(2) = {(x,y) in N xx N: x + 2y = 10} , Then

Let R be a relation on N defined by R={(x,y):2x+y=10}, then domain of R is

Find the domain and range of the following relation R={(x,y):x in N ,x lt 6 and y=4}

Find the middle in the expansion of : (i) (x/3 + 9y)^10 (ii) (x/y + y/x)^(2n+1)

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let N be the set of all natural numbers and let R be a relation on N×N...

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  2. Let R be a relation on the set of all line in a plane defined by (l1, ...

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  3. Each of the following defines a relation on N: x -> y , (i) x , y in ...

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  4. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  5. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  6. Let A={1,2,3,.....,9} and R be the relation in AxxA defined by (a ,b)R...

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  7. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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  8. Let n be a positive integer. Prove that the relation R on the set Z o...

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  9. Let "T" be the set of all triangles in a plane with "R" as relation ...

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  10. If R and S are relations on a set A , then prove the following :...

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  11. Let S be a relation on the set R of all real numbers defined by S=...

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  12. Write the domain of the relation R defined on the set Z of integers as...

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  13. If R and S are transitive relations on a set A , then prove that...

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  14. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given ...

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  15. If R={(x,y):x+2y=8} is a relation on N, write the range of R.

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  16. Let Z be the set of all integers and R be the relation on Z defi...

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  17. The union of two equivalence relations on a set is not necessarily an ...

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  18. Let A be the set of all students of a boys school. Show that the re...

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  19. Prove that a relation R on a set A is symmetric iff R=R^(-1) .

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  20. The relation R on the set N of all natural numbers defined by (x ,\ y)...

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