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

Show that the relation R on the set A={1, 2, 3, 4, 5} given by R={(a,b): abs(a-b) is even} in an equivalence ralation.

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

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ARIHANT PUBLICATION-SAMPLE PAPER 3 -SHORT ANSWER TYPE QUESTIONS
  1. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  2. Answer any one question : Evaluate int(0)^(3) (2x^(3) + 3x +5) dx .

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  3. Let f : R to R be a function given by f (x) = ax + b for all x in R. F...

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  4. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  5. Answer the question : Evaluate int(2x^(3) + 3x^(2) +5) dx

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  6. If A = [{:(0,2),(3,-4):}] and KA = [{:(0, 3a),(2b, 24):}], then find v...

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  7. Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (...

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  8. Find the inverse of the following matrix [{:(1,3,-2),(-3,0,-1),(2,1,...

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  9. A card from a pack of 52 playing cards is lost. From the remaining car...

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  10. How many times must a man toss a fair coin so that the probability of ...

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  11. If f(x+y) = f(x) f(y) for all x,y and if f(5) = 2 and f(0) = 3, then w...

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  12. Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if ...

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  13. Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...

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

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  15. If x = 3 sin t - sin 3t, y = 3 cos t - cos 3t, find (dy)/(dx) at t = (...

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  16. Evaluate int(2x^(3) + 3x^(2) +5x+2) dx

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  17. Solve the following differerntial equation x (dy)/(dx) + y = x cos x +...

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  18. Evaluate int (x ^(2) +1)/( (x +1) ^(2)) dx

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  19. Evaluateint (cosxtan x )/((sec x + tan x )) dx

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  20. Find the area of region included between the parabola 4y = 3x^(2) and ...

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