Course Area Covered
- i) Finite & Infinite Sets
- ii) Null & Singleton Sets
- iii) Equal & Equivalent Sets
- iv) Subsets, Proper & Improper — Formula \(2^n,\; 2^n-1\)
- v) Universal Sets
Bloom's Level:
K – Knowledge
U – Understanding
A – Application
HA – Higher Ability
Grid 1
Specification Grid – 1
| Level | No. of Questions | Marks |
|---|---|---|
| K | 1 | 1 |
| U | 1 | 1 |
| HA | 1 | 1 |
| Total | 3 | 3 |
1
Teacher asked Rinku to make 4 sets on a white board named as \(A, B, C, D\).
\(A = \{2, 4, 6, 8\}\)
\(B = \{a, b, c, d\}\)
\(C = \{4, 6\}\)
\(D = \{x : x \text{ is a prime number between 8 and 10}\}\)
- a Which set is an example of a null set? [1K]
- b Which set is a proper subset of \(A\)? [1U]
- c Explain, why set \(A\) and \(B\) are equivalent but not equal? [1HA]
2
Prem Sir wrote these sets on a white board.
\(P = \{1, 5, 6, 8\}\)
\(Q = \{2, 4, 7, 9\}\)
\(R = \{10\}\)
\(S = \{3, 10\}\)
- a Which set is an example of a singleton set? [1K]
- b Write the universal set \(U\) related to sets \(P, Q, R, S\). [1U]
- c Explain the relation between sets \(R\) and \(S\). [1HA]
Grid 2
Specification Grid – 2
| Level | No. of Questions | Marks |
|---|---|---|
| K | 1 | 1 |
| U | 1 | 1 |
| A | 1 | 1 |
| Total | 3 | 3 |
3
If \(A = \{2,4,6,8\}\), \(B = \{4,6,8\}\), \(C = \{6,4,2,8\}\), \(D = \{1,4,6,8\}\)
- a Which set is an improper subset of \(C\)? [1K]
- b Write any two subsets of \(B\) containing 2 elements only. [1A]
- c Differentiate with examples between finite and infinite sets. [1U]
4
\(P = \{x : 2 < x < 5\}\), \(Q = \{x : x \text{ is an even number}\}\), \(R = \{x : x \text{ is a prime number less than 10}\}\)
- a Write sets \(P\) and \(R\) in roster form. [1K]
- b Out of these three sets, which set is an infinite set? [1U]
- c Set \(S = \{2, 3, 5, a-2\}\) and it is equal to set \(R\). Find the value of \(a\). [1A]
Grid 3
Specification Grid – 3
| Level | No. of Questions | Marks |
|---|---|---|
| K | 1 | 1 |
| A | 1 | 1 |
| HA | 1 | 1 |
| Total | 3 | 3 |
5
Basanti wrote these sets on her copy.
\(A = \{a,b,c,d\}\), \(B = \{b,c\}\), \(C = \{\}\), \(D = \{d,b,a,c\}\)
\(A = \{a,b,c,d\}\), \(B = \{b,c\}\), \(C = \{\}\), \(D = \{d,b,a,c\}\)
- a Which set is equal to set \(A\)? [1K]
- b Write all possible subsets of set \(B\). [1A]
- c A set has 7 proper subsets. How many elements are there in that set? [1HA]
6
Rajjo was asked to write 4 different sets. She wrote:
\(A = \{1,3,5\}\)
\(B = \{2,3,4,5\}\)
\(C = \{6,7\}\)
\(D = \{8,9,10\}\)
- a Write a formula to calculate the number of possible subsets \((n)\). [1K]
- b Write an improper subset of set \(D\). [1A]
- c "All equal sets are equivalent sets but not all equivalent sets are equal sets." Explain this statement with examples. [1HA]
Additional Questions
New
7
Sunita listed the following sets during her maths class:
\(P = \{x : x \text{ is a vowel in the word "SCHOOL"}\}\)
\(Q = \{o\}\)
\(R = \{x : x \text{ is a letter of the English alphabet}\}\)
\(S = \{a, e, i, o, u\}\)
- a Write set \(P\) in roster form. Is \(P\) a singleton set? [1K]
- b Is \(P\) a subset of \(S\)? Justify your answer. [1U]
- c How many proper subsets does set \(S\) have? Use the formula and verify by listing all subsets of \(Q\). [1HA]
New
8
A teacher wrote the following sets on the board and asked students to analyse them:
\(A = \{1, 2, 3, 4, 5\}\)
\(B = \{x : x \text{ is a natural number less than 6}\}\)
\(C = \{2, 4, 6, 8, \ldots\}\)
\(D = \{0\}\)
- a State whether \(C\) is a finite or infinite set. Give a reason. [1K]
- b Are sets \(A\) and \(B\) equal sets? Show your working. [1U]
- c Is \(D\) a null set? Explain the difference between a null set and a set containing zero. [1HA]
New
9
Ramesh wrote these sets during his homework:
\(X = \{3, 6, 9, 12\}\)
\(Y = \{12, 9, 6, 3\}\)
\(Z = \{p, q, r, s\}\)
\(W = \{3, 6\}\)
- a Are \(X\) and \(Y\) equal sets? State the rule you used. [1U]
- b Write the universal set \(U\) that includes all elements of \(X, Z,\) and \(W\). [1K]
- c Are sets \(X\) and \(Z\) equivalent? Are they equal? Explain how two sets can be equivalent without being equal. [1HA]
New
10
Consider the following sets:
\[M = \{x : x \text{ is a factor of } 12\}, \quad N = \{1, 2, 3, 4, 6, 12\}, \quad K = \{1, 2, 3\}\]
- a Write set \(M\) in roster form and state its cardinality \(n(M)\). [1K]
- b Is \(K\) a proper subset of \(M\)? Calculate the total number of proper subsets of \(M\) using the formula. [1U]
- c A student says "\(M\) and \(N\) are equal sets." Another says "They are only equivalent." Who is correct and why? Write the improper subset of \(N\) as well. [1HA]