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A relation R is defined from {2,3,4,5,}...

A relation `R` is defined from `{2,3,4,5,}` to{3, 6, 7, 10}by `: x R y :x` is relatively prime to `ydot` Then, domain of `R` is (a)`{2,3,5,}` (b) `{3,5,}` (c) `{2,3,4,}` (d) `{2,3,4,5,}dot`

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To solve the problem, we need to determine the domain of the relation \( R \) defined from the set \( \{2, 3, 4, 5\} \) to the set \( \{3, 6, 7, 10\} \) where \( x R y \) means \( x \) is relatively prime to \( y \). ### Step-by-Step Solution: 1. **Understanding Relatively Prime**: Two numbers \( x \) and \( y \) are relatively prime if their greatest common divisor (gcd) is 1. This means they do not share any prime factors. 2. **Evaluate Each Element in the Domain**: ...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  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. A relation R is defined from {2,3,4,5,} to{3, 6, 7, 10}by : x R y :...

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

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

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  6. Let A={-1,3,5} and B={2,3} find the following products (i) AxxB (ii) ...

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

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

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

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

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  11. If A={1,2},B={3,4}a n dC={4,5,6}dotT h e n , AxxB={1,2}xx{3,4}={(1,3)...

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  12. Findxa n dy , if (x+3,5)=(6,2x+y)dot

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  13. If A={a ,b} and B={1,2,3}, find AxxB ,BxxA and (AxxB)nn(BxxA)

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

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  15. A relation R is defined from a set A={2,3,4,5} to a set B=3,6,7,10 as ...

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

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  17. For any three sets A ,B ,C prove that: A-(B uu C)=(A-B)nn(A-C)

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  18. Theorem 9(A and B are two non empty set having n element in common ; t...

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  19. Let A be a non-empty set such that AxxB=AxxC . Show that B=C .

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

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