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

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`.

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RD SHARMA ENGLISH-RELATIONS-All Questions
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  2. If R1 and R2 are equivalence relations in a set A, show that R1nnR2...

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

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

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  5. An integer m is said to be related to another integer n if m is a mult...

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  6. Show that the relation geq on the set R of all real numbers is r...

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  7. m is said to be related to n if m and n are integers and m-n is divisi...

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

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  9. Show that the relation R defined by R={(a , b):a-b is divisible ...

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

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  11. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

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  12. Let a relation R1 on the set R of real numbers be defined as (a , b) ...

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  14. The following relation is defined on the set of real number: a R ...

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  15. Prove that every identity relation on a set is reflexive, but the c...

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  16. Let R be a relation defined on the set of natural numbers N as R={(...

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  17. Let N denote the set of all natural numbers and R be the relation on N...

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

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