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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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SHARAM PUBLICATION-MODEL QUESTION PAPER -17-EXERCISE
  1. Find the general solution of the differential equation (1+x^2) tan^-1y...

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  2. Prove that f:RrightarrowR such that f(x)=frac[2x^2][x^2+1] is neither ...

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  3. Let A={1, 2, 3, 5}, B={4, 6, 9}, A relation R form A to B is defined b...

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  4. Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by ...

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  5. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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  6. Find the maixmum value of z =50x1+60x2 subject to 2x1+3x2le6,x1,x2ge0

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  7. Write the values of a and b, for which the vectors (a-1)hat(i) + (b+2)...

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  8. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

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  9. Find the co-ordinates of the point where the perpendicular from the or...

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  10. Find the equation of the plane passing through the line x = y = z and ...

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  11. Find the co-ordinates of the point where the line (x-2)/3=(y+1)/4=(z-2...

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  12. Find (dy)/(dx) when x^y+y^x=a^b

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  13. Evaluate inte^x((1+sinx)/(1+cosx))dx.

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  14. intsin^-1sqrt(x/(a+x))dx=.

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  15. Find the area of the region in the first quadrant bounded by x - axis,...

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

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  17. Solve: "tan"^(-1)(x-2)/(x-2) + "tan"^(-1) (x+1)/(x+2)=pi/4

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  18. Find graphically the maximum value of z = 2x + 5y subject to the const...

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  19. If veca,vecb and vecc are three vectors such that |veca|= 3,|vecb|= 4 ...

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  20. Find the coordinates of foot of perpendicular drawn from the point (0,...

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