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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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Show that the relation R on the set Z of integers given by R = {(a,b): 2 divides (a - b)} is an equivalence relation.

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SHARAM PUBLICATION-MODEL QUESTION PAPER 14-EXERCISE
  1. Find the extreme values of the function y = X + 1/x.

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  2. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

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  3. Integrate the following intsec^2sqrtx/sqrtxdx

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  4. intx^2tan^-1xdx

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  5. Solve (dy)/(dx)+y=e^(-x)

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  6. Using vector method find the area of the triangle with vertices (1, 0,...

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  7. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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  8. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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  9. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  10. Find the equation of the plane through the points (1, 2, -3), (2,3, -4...

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

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  12. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  13. Solve the following LPP graphically Maximize z=5x1+3x2 Subject to 3x1...

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  14. Show that |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}...

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  15. Examining consistency and solvability, solve the following equation by...

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  16. Find the point on the curve y^2-x^2 + 2x-1= 0 where the tangent is par...

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  17. Find the maximum of the function f(x)=(1/x)^x

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  18. Find intx^2(sin^4x+cos^4x)dx

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  19. solve:(1+y^2)xdx+(1-x^2)ydy=0

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  20. Prove that the two lines whose direction cosines are connected by the ...

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