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Let R be relation difined on the set of natural number N as follows, `R = { (x,y): x in N, y in N, 2x +y = 41}`. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive.

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The correct Answer is:
Domain ={1,2,3,……,20}
Range={39,37,35,….,3,1}
Relation is not reflexive, symmetric or transitive .
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NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS -Exercies 1a
  1. Give an example of a relation. Which is (i) Symmetric but neither r...

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  2. If A= {x,y,z}, B=(1,2,3} and R= {(x,2),(y,3),(z,1),(z,2), then find R^...

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  3. Prove that the relation R on Z defined by (a ,\ b) in RhArr a-b is di...

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  4. Prove that the relation R={(x,y): x, y in N and x-y " is divisible by ...

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  5. (i) Prove that the relation ""(x)R(y) iff 3 is a factor of (x-y) , de...

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  6. If I is the set of real numbers, then prove that the relation R={(x,y)...

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  7. If A={a,b,c,d}, then on A . (i) write the identity relation I(A) . ...

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  8. Show that the relation geq on the set R of all real numbers is ref...

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  9. Let O be the origin. We define a relation between two points P and ...

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  10. Let N be the set of all natural numbers and let R be a relation on Nxx...

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  11. (i) Show that in the set of positive integer, the relation ' greater t...

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  12. Show that the relation is congruent to on the set of all triangles ...

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  13. Show that the relation geq on the set R of all real numbers is ref...

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  14. Let R be relation difined on the set of natural number N as follows, R...

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  15. Let a relation R be defined by relation The R = {(4, 5), (1,4), (4, 6)...

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  16. If A={1,2,3,5}, B={2,4,6,8} and C={4,16,36,39} are three sets and R i...

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  17. Show that the relation R in the set R of real numbers, defined at R={...

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  18. If R1and R2are equivalence relations in a set A, show that R1nnR2is ...

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