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If BsubeA , show that BxxBsube(AxxB)nn(B...

If `BsubeA ,` show that `BxxBsube(AxxB)nn(BxxA)dot`

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Let us consider `(a,b) in (A×B)∩(B×A).`
`(a,b) in (A×B) and (a,b) in (B×A).`
`(a in A and b in B) and (a in B b in A).`
=`a,b in A and b,a in B`
=`(a,b) in (A xx B)`.....(1)
From (1)`BsubeA`=`(a,b) in BsubeA`
Now,`B xx B sube A xx A`...(2)
From(1) and (2) we have
...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Theorem 2 (For any three set A;B;C; prove that Axx(B-C)=(AxxB)-(AxxC)

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

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  3. If BsubeA , show that BxxBsube(AxxB)nn(BxxA)dot

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  4. If Aa n dB are any two non-empty sets, then prove that: AxxB=BxxA A=B...

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  5. If AsubeB , and CsubeD , prove that AxxCsubeBxxDdot

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  6. If AsubeB , prove that AxxCsubeBxxC for any set Cdot

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  7. If R is a relation on the set A={1,2,3,4,5,6,7,8,9} given by x R y, x ...

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  8. If A={1,2,3},B={4,5,6}, which of the following are relations from AtoB...

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

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

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

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

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

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

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

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

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

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

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

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