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Discrete Maths - Sets

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56. Let s(w) denote the set of al the letters in w where w is an English word. Let us denote set equality, subset and union relations by =, ⊂ and ∪ respectively.

Which of the following is NOT true?

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57. Let f : R → R be defined by

   f(x)=     {x+2       (x  ≤ -1)

               { x2         (-1  ≤ x  ≤1)

               {2 - x        (x  ≥ 1)

Then value of f (-1.75) + f (0.5) + f (1.5) is

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58. A relation R is defined on the set of positive integers as xRy
 if 2x + y  ≤ 5.

The relation R is

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59. Let R be an equivalence relation on the set {1,2,3,4,5,6} given by

{(1,1),(1,5),(2,2),(2,3),(2,6),(3,2),(3,3),(3,6),(4,4),(5,1),(5,5),(6,2),(6,6),(6,6)}.

The partition included by R is

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60. Which of the following sets is a null set ?

I.  X = {x | x= 9, 2x = 4 } 

II. Y = {x | x= 2x.x  ≠ 0 }


III. Z = { x | x-8  = 4 }

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