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Let Z be the set of all integers and Z0 ...

Let `Z` be the set of all integers and `Z_0` be the set of all non-zero integers. Let a relation `R` on `ZxxZ_0` be defined as follows: `(a ,\ b)\ R\ (c ,\ d)hArra d=b c` for all `(a ,\ b),\ (c ,\ d) in ZxxZ_0` Prove that `R` is an equivalence relation on `ZxxZ_0`

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Let Z be the set of all integers and Z_0 be the set of all non-zero integers. Let a relation R on ZxxZ_0 be defined as follows: (a , b)R(c , d) if and only if a d=b c for all (a , b),(c , d) in ZxxZ_0 Prove that R is an equivalence relation on ZxxZ_0 .

Let Z be the set of all integers and Z_0 be the set of all non zero integers. Let a relation R on Z X Z_0 be defined as follows: (a , b)R(c , d) ,a d=b c for all (a , b),(c , d) ZXZ_0 Prove that R is an equivalence relation on ZXZ_0dot

Let N be the set of all natural numbers and let R be a relation on NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ,\ b)R\ (c ,\ d) if a+d=b+c for all (a ,\ b),\ (c ,\ d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalence class [(2, 5)].

Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ,\ b)R\ (c ,\ d) if a+d=b+c for all (a ,\ b),\ (c ,\ d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalence class [(2, 5)].

Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) iff a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN is an equivalence relation. Also, find the equivalence classes [(2, 3)] and [(1, 3)].

Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Find the identity element in A .

Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If . is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Show that . is both commutative and associative on A

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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

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  3. Let Z be the set of all integers and Z0 be the set of all non-zero int...

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

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

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

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  7. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

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  8. Write the identity relation on set A={a ,\ b ,\ c} .

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  9. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

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

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  11. If R is a symmetric relation on a set A , then write a relation betwee...

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  12. Let R={(x ,\ y):|x^2-y^2|<1} be a relation on set A={1,\ 2,\ 3,\ 4,\ 5...

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  13. If A={1,2,\ 3,\ 4} , B={1,4,9,16,25} and R be a relation defined from ...

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  14. Let A={3,\ 5,\ 7} , B={2,\ 6,\ 10} and R be a relation from A to B def...

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  15. Define a reflexive relation.

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  16. Define a symmetric relation.

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  17. Define a transitive relation.

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  18. Define an equivalence relation.

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  19. If A={3,\ 5,\ 7} and B={2,\ 4,\ 9} and R is a relation given by "is l...

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  20. A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} and if R={(x ,\ y): y is one half of x ;...

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