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Let R be the relation on the Z of all in...

Let `R` be the relation on the `Z` of all integers defined by `(x ,y) in R x-y` is divisible by `n` . Prove that: `(x ,x) in R` for all `x in Z` `(x ,y) in R (y ,x) in R` for all `x ,y in Z` `(x ,y) in Ra n d(y , z) in R (x ,z) in R` for all `x ,y ,z in R`

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. If A={1,2,3},B={4,5,6}, which of the following are relations from AtoB...

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  2. A" "=" "{1," "2," "3." "5}" "a n d" "B" "=" "{4," "6," "9} . Define a ...

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  3. Let R be the relation on the Z of all integers defined by (x ,y) in R...

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  4. A relation R is defined from {2,3,4,5} to{3, 6, 7, 10}by : x R y :x i...

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  5. Let R be a relation in N defined by (x ,y) in R x+2y=8 . Express R a...

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  6. The Cartesian product A xxA has 9 elements among which are found (...

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  7. Let A={-1,3,5} and B={2,3} find AxxB

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  8. Express A={(a ,b):2a+b=5,a ,b in W} as the set ordered pairs.

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  9. If AxxB={(a ,1)(b ,3),(a ,3),(b ,1),(a ,2),(b ,2)}, find Aa n dBdot

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  10. Let A={1,2,3}and B={x : x in N ,x is prime less than 5}. Find AxxB

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  11. If AxxB={(a ,1)(a ,5),(a ,2),(b ,2),(b ,5),(b ,1)}, find BxxAdot

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  12. If A={1,2},B={3,4} find AxxB

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  13. Findx and y , if (x+3,5)=(6,2x+y)dot

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  14. If A={a ,b} and B={1,2,3}, find AxxB ,BxxA

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  15. If A={1,2,3},B={4},C={5}, then verify that: Axx(BuuC)=(AxxB)uu(AxxC)

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  16. If A={a ,b} and B={3}, find AxxB

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  17. If AxxBsubeCxxDa n dAxxB!=varphi, prove that AsubeC and BsubeD .

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  18. Express A={(a ,b):a+b=4,a ,b in W} as the set ordered pairs.

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  19. For any sets A ,B ,C ,D prove that: (AxxB)nn(CxxD)=(AnnC)xx(BnnD)

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  20. For any three sets A ,B ,C prove that: Axx(B^(prime)uuC^(prime))^'=(A...

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