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A" "=" "{1," "2," "3." "5}" "a n d" "B" ...

`A" "=" "{1," "2," "3." "5}" "a n d" "B" "=" "{4," "6," "9}` . Define a relation R from A to B by R = {(x, y): the difference between x and y is odd: `x in A ," "y in B` }. Write R in roster form.

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`A={1,2,3,5} and B={4,6,9}`
`R={(x,y):` the difference between x and y is odd `x∈A,y∈B}`
`∴R={(1,4),(1,6),(2,9),(3,4),(3,6),(5,4),(5,6)}`
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RD SHARMA-RELATIONS-Solved Examples And Exercises
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  2. If A={1,2,3},B={4,5,6}, which of the following are relations from AtoB...

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

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

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

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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 the following products (i) AxxB (ii) ...

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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 AxxBa...

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

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  13. Findxa n dy , 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 and (AxxB)nn(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. 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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  17. For any sets A ,B ,C ,D prove that: (AxxB)nn(CxxD)=(AnnC)xx(BnnD)

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

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

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

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