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If a set has n elements, how many relati...

If a set has n elements, how many relations are there from A to A?

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If a set A has n elements and another set B has m elements, what is the number of relations from A to B ?

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. If a set has n elements, how many relations are there from A to A?

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  2. Let A={1,2,3}, B={4,5}. Determine all relations from A to B.

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  3. Let A={1,2,3}, B={4,5}. Determine all relations from B to A.

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  4. Let A={1,2,3}, B={4,5}. Is there any relation which both a relation fr...

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  5. Let A={1,2,3}, B={4,5}. Determine all relations from A to A.

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  6. Let A={1,2,3}, B={4,5}. Determine all relations from B to B.

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  7. Mark the following as true (T) or false (F). phi is a relation from se...

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  8. Mark as true (T) or false (F). AtimesB is a relation from A to B

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  9. Mark as true (T) or false (F). phitimesphi is a relation from A to B

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  10. Mark as true (T) or false (F). A relation cannot be both symmetric ad ...

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  11. Mark as true (T) or false (F). For any equivalence relation R on a set...

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  12. Mark as true (T) or false (F). The relation R={(1,1),(2,2),(3,3)} on t...

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  13. What is the total number of relations from a set A to set B, where abs...

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  14. What is the partition of the set {1,2} induced by the equivalence rela...

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  15. Let R={(x,y):xlty,x,yinN}. Check if R is reflexive, symmetric or trans...

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  16. If a relation is symmetric and transitive on any non-empty set, then i...

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  17. Let R be a relation in the set of natural numbers N defined by xRy if ...

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  18. Write true or false in the following with reason or by suitable exampl...

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  19. Write true or false in the following with reason or by suitable exampl...

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  20. Compute the following remainder function. r3(185)

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