Write down the power set of the set {0}. ? {0} {?} {?, {0}} Let, A = {0}. The po

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Question
Write down the power set of the set {0}.
Options
A. ?
B. {0}
C. {?}
D. {?, {0}}

Correct Answer

{?, {0}}

Explanation

Let, A = {0}. The possible subsets of this set A are ? and {0}, so the power set of the given set A is P(A) = {f, {0}}.

Sets and Functions problems

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2.
Let A = {1, 3, 5} and B = {x: x is an odd natural number < 6}. Which of the following is false?
Options
A. A ? B
B. B ? A
C. A = B
D. None of these

3.
If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.
Options
A. U
B. A
C. ?
D. None of these

4.
If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ? B) ? (A ? C).
Options
A. {c}
B. {a}
C. {b}
D. {d}

5.
If A and B have n elements in common, how many elements do A � B and B � A have in common?
Options
A. n
B. n3
C. n2
D. None of these

6.
For which of the following cases A and B are equivalent?
Options
A. A = {a, b, c,?, z}, B = {1, 2, 3,?, 24}
B. A = {1/3,1/2,3/5}, B = { x : x = n/n+2, n ? N}
C. A = {2, 4, 6}, B = {(2, 4), (4, 6), (2, 6)}
D. A = { x : x = ( n3 - 1 )/ ( n3 + 1) , n ? W, n ? 3} , B = { 0,7/9,13/14}

8.
Which of the following sets is empty?
Options
A. A = {x: x ? n and x ? 1}
B. B = {x: 3x + 1 = 0, x ? N}
C. C = {x: x is an integer and -1 < x < 1}
D. D = set of months of the year beginning with F.

9.
Which of the following sets is finite?
Options
A. The set of the months of a year
B. {1, 2, 3,?}
C. {1, 2, 3,? 90, 100}
D. The set of lines which are parallel to x-axis

10.
Which of the following sets is finite?
Options
A. I = { x : x ? Z and x2 ? 2x ? 3 = 0 }
B. B = The set of natural numbers which are divisible by 2
C. C = The set of lines passing through a point.
D. D = { x : x ? Z and x > - 5 }

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