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The relation R on the set A = {1, 2, 3} ...

The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

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Show that the relation R in the set {1, 2, 3} defined as R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive, but neither symmetric nor transitive.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

If A = {1,2,3} and R = { (1,1}, ( 2,2), (3,3)} then R is reflexive, symmetric or transitive?

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Check whether the relation R defined in the set {1, 2,3,4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Show that the relation R in the set {1,2,3} defined as R={(1,3), (3, 2), (1, 2)} is transitive but neither reflexive nor symmetric.

Let A = (1,2,3) and R = (1,1), (2,2), (1,2), (2,1), (1,3) then R is

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A be a finite set. Then, each injective function from A into itsel...

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  2. True or False statements : Let A = (a,b,c) and R = (a,b),(a,c). Then...

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  3. The relation R on the set A = {1, 2, 3} defined as R = {(1, 1), (1, 2)...

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  4. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  5. Every relation which is symmetric and transitive is also reflexive.

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  6. True or False statements : Let N be the set of natural numbers. Then...

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  7. True or False statements : A binary operatio on a set has always the...

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  8. The function f : R rarr R defined by f(x) = 1 + x^2 is :

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  9. True or False statements : Let N be the set of natural numbers. Then...

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  10. True or False statements : The function f : R rarr R defined by f(x)...

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  11. Let A = {0, 1} and N be the set of natural numbers. Then the mapping f...

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  12. True or False statements : The binary operation * defined in Z by a ...

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  13. An integer m is said to be related to another integer n if m is a inte...

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  14. Let R be a relation from a set A to a set B, then:

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  15. True or False statements : Composition of functions is associative.

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  16. True or False statements : The function f : R rarr R defined by f(x)...

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  17. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  18. Let f : A rarr B and g : B rarr C be onto functions, show that gof is ...

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  19. For all sets A, B and C, if A⊂ C and B ⊂ C,then A∪ B ⊂ C.

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  20. Match the following : .

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