Let X be a non-empty set and let A, B, C be sub sets of X. Consid

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Consider the following statements for the two non-empty sets A and B :

1. A  B  A  B  A  B = A  B2. A  A  B = A  B

Which of the above statements is/are correct ?

  • 1 only

  • 2 Only

  • Both 1 and 2

  • Neither 1 nor 2


2.

If A = λ, λ, μ, then the power set of A is :

  • ϕ, ϕ, λ, λ, μ

  • ϕ, λ, λ, μ, λ, λ, μ

  • ϕ, λ, λ, μ, λ, λ, μ

  • λ, λ, μ, λ, λ, μ


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3.

Let X be a non-empty set and let A, B, C be sub sets of X. Consider the following statements :

1.A  C  A  B  C  B, A  B  C  B

2. A  B  C  B for all sets B  A  C

3. A  B  C  B for all sets B  A  C

Which of the statements are correct ?

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


D.

1, 2 and 3

Here A  X  All elements of  belongs to XB  X  All elements of  belongs to X and

 C   X  All elements of  belongs to X X is Universal set1. A  B  A  B  C  BA  B  C  B 

First
 statement is True2. A  B  C  B  For all B  A  C Second statement is also true3. A U B  C  B  Third statement is also true


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4.

Consider the following statements:

  1. The algebraic sum of deviations of a set of values from their arithmetic mean is always zero.
  2. Arithmetic mean > Median > Mode for a symmetric distribution.                                                          Which of the above statements is/are correct ?

  • 1 Only

  • 2 Only

  • Both 1 and 2

  • Neither 1 nor 2


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5.

Let A and B be subsets of X and C = (A  B')  (A'  B), where A' and B' arecomplements of A and B respectively in X. What is C equal to?

  • (A  B') - (A  B')

  • A'  B - A'  B

  • A  B - A  B

  • A'  B' - A'  B' 


6.

If A, B and C are subsets of a Universal set, then which one of the following is not correct ?

  • A  B  C = A  B  A  C

  • A'  A  B = B'  A'  A

  • A'  B  C = C'  B'  A'

  • A  B  C = A  C  B  C


7.

Let A = x R : - 1  x  1,      B = y  R : - 1  y  1 and S be the subset of A × B, defined by      S = x, y  A × B : x2 + y2 = 1Which one of the following is correct ?

  • S is a one-one function from A into B

  • S is a many-one function from A into B

  • S is a bijective mapping from A into B

  • S is not a function


8.

Two integers x and y are chosen with replacement from the set [0, 1, 2, ..., 10]. The probability that x - y > 5 is

  • 611

  • 35121

  • 30121

  • 25121


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9.

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then, the number of subsets of A containing two or three elements is

  • 45

  • 120

  • 165

  • 330


10.

Consider the following in respect of sets A and B : 1. A  B  B = A2. A - B  A = A3. A - B  B = ϕ4. A B  A  B = BWhich of the above are correct ?

  • 1, 2 and 3

  • 2, 3 and 4

  • 1, 3 and 4

  • 1, 2 and 4


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