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R is relation in N xxN as (a,b) R (c,d) ...

R is relation in `N xxN` as (a,b) R (c,d) `hArr ad = bc`. Show that R is an equivalence relation.

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Prove that a relation R defined on NxxN where (a, b)R(c, d) ad = bc is an equivalence relation.

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

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.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Let A = {1,2,3.......9} and R be the relation in AxxA defined by (a,b) R , (c,d) if a + d = b + c for (a,b) , (c,d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalent class [(2,5)].

Let f: X rarrY be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)} . Examine whether R is an equivalence relation or not.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxNdot

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. The relation R difined the set Z as R = {(x,y) : x - yin Z} show that ...

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  2. Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c...

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  3. R is relation in N xxN as (a,b) R (c,d) hArr ad = bc. Show that R is a...

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  4. The relation R defined in the set N of natural number as AAn,minN if o...

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  5. Find the domain and range of the following function : f : R rarr R ...

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  6. Find the domain and range of the following function : f : R rarr R ...

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  7. Find the domain and range of the following function : f: R rarr R ,...

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  8. Find the domain and range of the following function : f : R rarr R...

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  9. Find the domain and range of the following function : f: R rarr R ,...

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  10. f:R rarr R , f(x) = {(12x+5,x gt1),(x-4,xle1):} then find f(0),f(-1/2)...

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  11. Check the injectivity and surjectivity of the following functions . ...

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  12. Check the injectivity and surjectivity of the following functions . ...

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  13. Check the injectivity and surjectivity of the following functions . ...

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  14. Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) ...

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  15. f:Z rarrZ , f(n) ={{:((n+2)," if n is even"),((2n+1)," if n is odd" )...

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  16. f:NxxNrarrN , f("(m,n)")=m+n . If f one one and onto ?

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  17. Show that f: R rarr R , f(x) = x/(x^(2)+1) is not one one and onto fun...

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  18. f: R rarr R , f(x) =x^(2)+1. Find the preimage of 17 and -3.

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  19. f : R rarr R , f(x) ={{:(2x,xgt3),(x^2,1ltxle3),(3x,xle1):} then find...

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  20. Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is de...

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