Sample QuestionsSets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Suppose A1, A2, ..., A30 are thirty sets each having 5 elements and B1, B2, ..., Bn are n sets each with 3 elements, let $\bigcup\limits_{\text{i}=1}^{30}\text{A}_\text{i}=\bigcup\limits_{\text{j}=1}^\text{n}\text{B}_\text{j}=\text{S}$ and each element of S belongs to exactly 10 of the Ai ’s and exactly 9 of the B, 'S. then n is equal to.
- 15
- 3
- 45
- 35
Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to,
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$\text{F}_2\cap\text{F}_3$
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$\text{F}_3\cap\text{F}_4$
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$\text{F}_2\cup\text{F}_5$
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$\text{F}_2\cup\text{F}_3\cup\text{F}_4\cup\text{F}_1$
The set $(\text{A} \cap \text{B}')' \cup (\text{B} \cap \text{C})$ is equal to.
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$\text{A}'\cup\text{B}\cup\text{C}$
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$\text{A}'\cup\text{B}$
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$\text{A}'\cup\text{C}'$
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$\text{A}'\cap\text{B}$
If X = {8n - 7n - 1 | n $\in$ N} and Y = {49n - 49 | n $\in$ N}. Then
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$\text{X} \subset \text{Y}$
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$\text{Y} \subset \text{X}$
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$\text{X} = \text{Y}$
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$\text{X} \cap \text{Y} = \phi$
Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then
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$\text{S}\cap\text{T}\cap\text{C}=\phi$
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$\text{S}\cup\text{T}\cup\text{C}=\text{C}$
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$\text{S}\cup\text{T}\cup\text{C}=\text{S}$
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$\text{S}\cup\text{T} = \text{S}\cap\text{C}$
Let sets R and T be defined as
R = {x $\in$ Z | x is divisible by 2}
T = {x $\in$ Z | x is divisible by 6}. Then $\text{T} \subset \text{R}.$
View full solution →If A is any set, then $\text{A} \subset \text{A}.$
View full solution →Given A = {0, 1, 2}, $\text{B} = {\text{x} \in \text{R} | 0 \leq \text{x} \leq 2}.$ Then A = B
View full solution →$\text{Q} \cup \text{Z} = \text{Q},$ where Q is the set of rational numbers and Z is the set of integers.
View full solution →Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then $\text{B} \not\subset \text{M}.$
View full solution →Power set of the set A = {1, 2} is ______________.
When $\text{A}=\phi,$ then number of elements in P(A) is ______________.
View full solution →The set $\{\text{x} \in \text{R} : 1 \leq \text{x} < 2\}$ can be written as ______________.
View full solution →If A and B are finite sets such that $\text{A}\subset\text{B},$ then $\text{n} (\text{A} \cup \text{B})$ = ______________.
View full solution →Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______________.
If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a is less that 6 and $\text{a} \in \text{Y}$
View full solution →If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
$\text{a} \in \text{Y}$ but $\text{a}^2 \notin \text{Y}.$
View full solution →Write the following sets in the roaster from.
C = {x | x is a positive factor of a prime number p}.
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
n - 1.
Given that N = {1, 2, 3, ..... , 100}. Then write.
The subset of N whose element are perfect square numbers.
For all sets A, B and C, if $\text{A}\subset\text{B},$ then $\text{A}\cap\text{C}\subset\text{B}\cap\text{C}$
View full solution →For all sets A, and B, $\text{A}-(\text{A}\cap\text{B})=\text{A} - \text{B}.$
View full solution →Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}
Verify that $\text{L}-(\text{M}\cup\text{N})=(\text{L}-\text{M})\cap(\text{L}-\text{N})$
View full solution →If Y = {x | x is a positive factor of the number 2p - 1 (2p - 1), where 2p - 1 is a prime number}.Write Y in the roaster form.
State the following statement is true and false. Justify your answer.
496 $\notin$ {y | the sum of all the positive factors of y is 2y}.
View full solution →Let $\text{T}=\Big\{\text{x}|\frac{\text{x}+5}{\text{x}-7}-5=\frac{4\text{x}-40}{13-\text{x}}\Big\}.$ Is T an empty set? Justify your answer.
View full solution →If A and B are subsets of the universal set U, then show that.
$\text{A} \subset \text{A} \Leftrightarrow \text{A}\cap\text{B}=\text{B}$
View full solution →For all sets A, B and C, show that $(\text{A} - \text{B}) \cap (\text{C} - \text{B}) = \text{A} - (\text{B} \cup \text{C})$
Determine whether each of the statement in Exercises 13 - 17 is true or false. Justify your answer.
View full solution →In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find
- The number of families which buy newspaper A only.
- The number of families which buy none of A, B and C.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed.
- In English and Mathematics but not in Science.
- In Mathematics and Science but not in English.
- In Mathematics only.
- In more than one subject only.
Match the following sets for all sets A, B and C. | (i) | $((\text{A}'\cup\text{B}')-\text{A})'$ | (a) | $\text{A} - \text{B}$ |
| (ii) | $[\text{B}'\cup(\text{B}'-\text{A})]'$ | (b) | $\text{A}$ |
| (iii) | $(\text{A} - \text{B}) - (\text{B} - \text{C})$ | (c) | $\text{B}$ |
| (iv) | $(\text{A}-\text{B})\cap(\text{C}-\text{B})$ | (d) | $(\text{A}\times\text{B})\cap(\text{A}\times\text{C})$ |
| (v) | $\text{A}\times(\text{B}\cap\text{C})$ | (e) | $(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$ |
| (vi) | $\text{A}\times(\text{B}\cup\text{C})$ | (f) | $(\text{A}\cap\text{C})-\text{B}$ |
View full solution →Let A, B and C be sets. Then show that $\text{A}\cap(\text{B}\cup\text{C})=(\text{A}\cap\text{B})\cup(\text{A}\cap\text{C}).$
View full solution →