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If Z is the set of all integers and R i...

If Z is the set of all integers and R is the relation on Z defined as `R={(a, b): a, b in Z and a-b` is divisible by 3. Prove that R is an equivalence relation.

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If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let n be a fixed positive integer. Define a relation R on Z as follows for all a, b in Z, aRb, if and only if a-bis divisible by n. Show that R is an equivalence relation.

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Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

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The ralation R on Z is defined by for m, nin Z , mRnimpliesm/n is a power of 2. Examine whether it is an equivalence relation.

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SHARAM PUBLICATION-MODEL QUESTION PAPER-3-EXERCISE
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  2. If the cartesian equation of a line is (3-x)/5=(y+4)/7=(2z-6)/4 then w...

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  3. If Z is the set of all integers and R is the relation on Z defined as...

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  4. If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} i...

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  5. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

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  6. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  7. Sole the following LPP graphically Maximise Z=6x(1)+7x(2) Subject ...

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  8. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  9. Using elementary operation find the inverse of [(2,3),(5,7)]

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  10. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  11. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  12. Find the value of k if the function f(x) defined by f(x)={(2x-1,when x...

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  13. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

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  14. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  15. Find the equations of the tangent to the curve x = sin 3t, y = cos 2t ...

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  16. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  17. Evaluate the following integrals : int(cos^(-1)x)/(sqrt(1-x^(2)))dx.

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  18. Evaluate int(sin x - cos x)dx.

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  19. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  20. Determine the area the of the region between the curves y=cos x and y=...

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