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Let R be a relation on the set A of orde...

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv= yu. Show that R is an equivalence relation.

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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Show that the VV: RxxR rarr R given by (a, b) rarr max {a, b} and th...

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  2. Show that + : Rxx R rarr R and xx: R xxR rarr R are commutative binar...

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  3. Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commuta...

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  4. Show that addition and multiplication are associative binary operation...

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  5. Show that ""^** : R xxR rarr R given by a^** b rarr a + 2b is not ass...

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  6. Show that zero is the identity for addition on R and 1 is the identity...

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  7. Show that -a is the inverse of a for the addition operation '+' on R...

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  8. Show that -a is not the inverse of a in N for the addition operation...

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  9. If R1 and R2 are equivalence relations in a set A, show that R(1) cap...

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  10. Let R be a relation on the set A of ordered pairs of positive integers...

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  11. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R1 be a relation in X given ...

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  12. Let f: X rarrY be a function. Define a relation R in X given by R = {...

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  13. Determine which of the following binary operations on the set R are as...

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  14. Determine which of the following binary operations on the set R are as...

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  15. Find the number of all one-one functions from set A = {1, 2, 3} to its...

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  16. Let A = {1, 2, 3} Then show that the number of relations containing (1...

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  17. Show that the number of equivalence relation in the set {1, 2, 3} cont...

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  18. Show that the number of binary operations on {1, 2} having 1 as identi...

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  19. Consider the identity function I(N) : N rarr N defined as I(N) (x) = ...

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  20. Consider a function f : [0,(pi)/2]rarrR given by f(x) = sin x and g :...

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