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Show that the relation S defined on set ...

Show that the relation S defined on set `N xx N` by `(a, b) S(c,d) rArr a+d=b+c` 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.

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MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. If |vec a.vec b|=|vec axxvec b| then angle between them is.

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  2. Find the value of lambda so that the vectors veca and vecb are perpend...

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  3. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  4. A trust fund has Rs. 50,000 that is to be invested in two types of ...

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  5. Find the inverse of the following matrices using elementary transforma...

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  6. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  7. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  8. If y=In(x^2 +y^2),then find dy/dx.

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  9. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  10. Test the differentiability and continuity of the following function at...

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  11. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  12. int0^piabs(cosx)dx

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  13. Solve :(1 + y^2).dx+xdy = tan^-1y dy

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  14. A plane meets the coordinate axes at A, B and C respectivély. If the c...

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  15. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  16. Prove that the acute angle between the lines whose direction cosines a...

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  17. Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...

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  18. Constract the composition table/multiplication table for the binary op...

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  19. Let A = ( ( 1 2 2) , (2 1 2), (2 2 1)).Find A^-1 and hence show A^2-4A...

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  20. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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