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Find whether the following statements ar...

Find whether the following statements are true or false. If the statement is false, then write its correct statement:
(i) If P={m,n} and Q={n,m},then `PxxQ={(m,n),(n,m)}`.
(ii) If A and B are non-empty sets, then `AxxB` is a non-empty set of the ordered pairs (x,y) such that `x in A and y in B`.

Text Solution

Verified by Experts

The correct Answer is:
`A=(-1,0,1}`
`AxxA={(-1,-1),(-1,0),(-1,1),(0,0),(0,1),(1,-1),(1,1)}`
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS-Exercise 2A
  1. If ((x)/(3)+1 ,y-(2)/(3))=((5)/(3)/(1)/(3)), then find the values of x...

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  2. Find the values of x and y from each of the following (i) (x+y,x-2y)...

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  3. If A={2,-3} and B={1,3,5}, then find AxxB and BxxA.

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  4. If A ={1,2}, then find AxxAxxA.

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  5. If A={x,y,z} and B={2,3}, then find AxxB.

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  6. If A ={1,2,3,4} and B={x:x in N and x, is a prime number less than 5},...

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  7. If AxxB={(a,3),(a,5),(b,3),(b,5),(c,3),(c,5)}, then find BxxA.

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  8. Find whether the following statements are true or false. If the statem...

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  9. The Cartesian product A xxA has 9 elements among which are found (1...

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  10. If AxxB={(a,2),(b,4),(a,6),(b,2),(b,6),(a,4)}, then find A and B.

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  11. If A={1,2,3}, B={3,4} and C={4,5,6}, then find each of the following :...

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  12. If A={1,2,3,4,5}, B={1,2,3,6,7} and C{8}, then find (A-B)xx C.

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  13. If A={1,2} and B={x,y}, then find AxB. Also find the number of its sub...

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  14. If A={-1,1}, then find AxxAxxA.

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  15. If A={1,2,3} and B={1,2}, then represent AxxB graphically.

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  16. If A ={x,y,z} and B={5,6}, then represent each of the following by arr...

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  17. The set A and B has 3 common elements . If n(A) =5 and n(B)=4, then fi...

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  18. sube B, then prove that AxxA sube (AxxB) nn (BxxA).

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

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