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 $\bigcup\limits^{30}_\text{i = 1}\text{A}_\text{i}=\bigcup\limits^{\text{n}}_\text{j = 1}\text{B}_\text{j}=\text{S}$ and each element of S belong to exactly 10 of the Ai's and exactly 9 of the Bj's, then n is equal to:
- 15
- 3
- 45
- 35.
View full solution →If A and B are two sets such that $\text{n(A)}=70, \text{ n(B)}=60, \text{ n(A}\cup\text{B)}=110,$ then $\text{n(A}\cap\text{B)}$ is equal to:
- 240
- 50
- 40
- 20.
View full solution →For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}=$
-
A
-
B
-
$\phi$
-
None of these.
View full solution →If A = {1, 3, 5, B} and B = {2, 4}, then:
- $4\in\text{A}$
- $\{4\}\subset\text{A}$
- $\text{B}\subset\text{A}$
- None of these.
View full solution →Let A and B be two sets that $\text{n(A)} = 16, \text{ n(B)} = 14,\text{ n(A}\cup\text{B)}=25.$ Then, $\text{n(A}\cap\text{B)}$ is equal to:
- 30
- 50
- 5
- None of these.
View full solution →Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\phi\in \text{A}$
View full solution →The given statements is corect? Write a correct form of the given incorrect statements. $\{\text{b, c}\}\subset\{\text{a},\{\text{b, c}\}\}$
View full solution →Let $\text{A}=\{\phi,\{\phi\},1\{1,\phi\},2\}.$ Then the statement is true?
$\{\{2\},\{1\}\}\not\subset\text{A}.$
View full solution →The given statements is corect? Write a correct form of the given incorrect statements.
$\phi\subset \{\text{a, b, c}\}$
View full solution →State whether the following statements are true or false:
The set {x : x + 8 = 8} is the null set.
If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
-4 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
9 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
-2 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
4 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
12 ...... A.
View full solution →The given collections are sets or not? Justify your answer:
The collection of most talented writers of India.
If A = {(x, y) : y = ex, x $\in$ R} and B = {(x, y) : e-x, x $\in$ R}, then write $\text{A}\cap\text{B}.$
View full solution →How many elements has P(A), if $\text{A}=\phi$?
View full solution →The given following sets are finite & in which of it infinite in if?
Set of letters of the English Alphabets;
The given following sets are finite & in which of it infinite in if?
$\{\text{x}\in\text{N}:\text{x}<5\}$
View full solution →Write the sets $\Big\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\Big\}$ in the set-builder form.
View full solution →If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find:
$(\text{A}\cap\text{B})\cap(\text{B}\cap\text{C})$
View full solution →Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}. Verify the following identities:
$\text{A}\cup(\text{B}\cap\text{C})=(\text{A}\cup\text{B})\cap(\text{A}\cup\text{C})$
View full solution →Describe the following sets in set-builder form:
A = {1, 2, 3, 4, 5, 6}
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find:
$\text{A}\cup\text{B}\cup\text{D}$
View full solution →If A and are sets, then prove thet $\text{A - B},\text{ A}\cap\text{B}$ and $\text{A - B}$ are pair wise disjoint.
View full solution →Show that for any sets A and B, $\text{A}=(\text{A}\cap\text{B})\cap(\text{A - B})$
View full solution →Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, and C = {3, 4, 5, 6}. Find:
- A'
- B'
- $(\text{A}\cap\text{C})'$
- $(\text{A}\cup\text{B})'$
- (A')'
- (B - C)'.
View full solution →Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find:
$\text{B}\cap\text{C}$
View full solution →In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 physics and mathematics. How many teach physics?
Show that for any sets A and B, $\text{A}\cup(\text{B}-\text{A})=(\text{A}\cup\text{B})$
View full solution →For any two sets of A and B, prove that: $\text{A}'\cup\text{B}=\text{U}\Rightarrow\text{A}\subset\text{B.}$
View full solution →For any two sets A and B, prove that: $\text{A}\cap\text{B}=\phi\Rightarrow\text{A}\subseteq\text{B}'.$
View full solution →For any two sets of A and B, prove that: $\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$
View full solution →If A, B, C are three sets such that $\text{A}\subset\text{B},$ then prove that $\text{C} - \text{B}\subset\text{C} - \text{A}.$
View full solution →