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Let U = {1, 2, 3} and A, B and C be subsets of U. The statement C + A = (A – B) + C is NOT an identity.

Which one of the following alternatives contains sets A, B and C that can be used as counterexample to prove that the given statement not an identity.

  •  A. A = {1}, B = {2}, C = {3}
  •  B. A = {1}, B = {3}, C = {1, 2}
  •  C. A = {1, 2}, B = {2, 3}, C = {1, 2}
  •  D. A = {1}, B = { }, C = {3}

Suppose U = {1, {2, 3}, 3, d, {d, e}, e} is a universal set with the following subsets:

A = {{2, 3}, 3, {d, e}}, B = {1, {2, 3}, d, e} and C = {1, 3, d, e}.

Let S = {(1, 3), (1, d), (1, e), (d, e), (3, d)} be a relation on set C.

Which one of the following statements regarding S is true?

  •  A. S is a strict total order.
  •  B. If (e, 3) is added to S, it would make S transitive.
  •  C. If (e, 3) is added to S, S would satisfy trichotomy.
  •  D. S is a weak partial order
  • Suppose U = {b, {c, 3}, 3, 4, {4, 5}, 5} is a universal set with the following subsets: A = {{c, 3}, 3, {4, 5}}, B = {b, {c, 3}, 4, 5} and C = {b, 3, 4, 5}. Let S = {(b, 3), (b, 4), (b, 5), (4, 5), (3, 4)} be a relation on set C. Which one of the following statements regarding S is true? 
  • A. If (5, 3) is added to S, S would satisfy trichotomy.
  •  B. S is a strict total order.
  •  C. S is a weak partial order.
  •  D. If (5, 3) is added to S, it would make S transitive.

Suppose U = {{a, b}, a, c, d, {a, d}, e} is a universal set with the following subsets:

A = {{a, b}, a, {a, d}}, B = {a, d, e} and C = {{a, b}, a, d, {a, d}, e}.

Which one of the following sets represents (A U B U C) – B ?

  •  A. {a, d, e}
  •  B. {{a, b}, a, d, e}
  •  C. {{a, b}, {a, d}}
  •  D. A U C

Consider a plane represented by the equation 11x+8y+6z+83=0. Find the distance of

this plane from origin. After that find the distance of this plane from a point P(6, 3, 3).


Consider a vector in 2D. The vector is represented by v(34, 25). If the vector is rotated

counterclockwise by an angle of 70 degree, what will be the rotated vector? Clearly

show your calculation.


Consider two lines L1 and L2. The parametric form for L1 is P1(3, 6, 9), V1(6, 9, 12).

The parametric form for L2 is P2(1, 4, 7), V2(11, 6, 12). Determine if the lines

intersect each other. If the lines intersect, find the intersecting point. If they do not

intersect, write how you deduced that.


Create a react single application:

- Components

o Home page (Default)

Create a good-looking home page add more items, sections

o About

Create resume, 

o Profile

Contact details - how can we reach you.

o Users

Create a list of users, store your users in an array

• Items [ name, surname, location, age]

• Display list of users based on their age (order by age)



1.)  Establish the initial feasible solutions of the LP model using NCR (North west Corner Rule), MCM ( Minimum Cost Method or Greedy Method), and VAM ( Vogel’s Approximation Method)

 Minimize: C = 14X1A + 25X1B + 13X1C + 18 X1D.+ 10X2A + 12X2B + 13X2C + 11X2D + 15X3A + 20X3B + 11X3C+ 25X3


   Subject to:  X1A + X1B + X1C + X1D = 140   X1A + X2A + X3A = 100

                      X2A + X2B + X2C + X2D = 160   X1B + X2B + X3B = 100

                      X3A + X3B + X3C + X3D = 50     X1C + X2C + X3C = 50

                      X1D + X2D + X3D = 100 Xij      


How do I do code for the number of words in a sentence
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