Chapter 1 -Sets

Revise Chapter Notes

Overview

This page provides comprehensive Class 11 Maths Exemplar Chapter 1 Exercise 1.2 Solutions. Detailed step-by-step solutions for Class 11 Maths NCERT Exemplar Chapter 1 Sets Exercise 1.2. Free PDF download and interactive practice.

Exercise 1.2

Short Answer Type Questions (1-4)

Q1
Write the following sets in the roster form:
(i) \(A = \{x : x \in R, 2x + 11 = 15\}\)
(ii) \(B = \{x | x^2 = x, x \in R\}\)
(iii) \(C = \{x | x \text{ is a positive factor of a prime number } p\}\)
Q2
Write the following sets in the roster form:
(i) \(D = \{t | t^3 = t, t \in R\}\)
(ii) \(E = \{w | \frac{w-2}{w+3} = 3, w \in R\}\)
(iii) \(F = \{x | x^4 - 5x^2 + 6 = 0, x \in R\}\)
Q3
If \(X = \{1, 2, 3\}\), if \(n\) represents any member of \(X\), write the following sets containing all numbers represented by
(i) \(4n\)
(ii) \(n+6\)
(iii) \(\frac{n}{2}\)
Q4
If \(Y = \{1, 2, 3, \dots, 10\}\), and \(a\) represents any element of \(Y\), write the following sets, containing all the elements satisfying the given conditions.
(i) \(a \in Y\) but \(a^2 \notin Y\)
(ii) \(a+1 \in Y\) and \(a-1 \in Y\)

Fill in the Blanks (5-13)

Q5
The set \(\{x \in R : 1 \le x < 2\}\) can be written as ________.
Q6
When \(A = \phi\), then the number of elements in \(P(A)\) is ________.
Q7
If \(A\) and \(B\) are finite sets, such that \(A \subset B\), then \(n(A \cup B)\) is equal to ________.
Q8
If \(A\) and \(B\) are finite sets, such that \(A \subset B\), then \(n(A \cap B)\) is equal to ________.
Q9
If \(A\) and \(B\) are any two finite sets, then \(n(A \cup B)\) is equal to ________.
Q10
\(A \cup B = A \cap B\) implies ________.
Q11
\((A \cup B)' = \) ________.
Q12
\((A \cap B)' = \) ________.
Q13
\((A \cup B) \cap (A \cup B') = \) ________.

True or False (14-19)

Q14
If \(A\) is any set, then \(A \subset A\).
Q15
If \(M = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\) and \(B = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}\), then \(B \not\subset M\).
Q16
The sets \(\{1, 2, 3, 4\}\) and \(\{3, 4, 5, 6\}\) are equal.
Q17
The sets \(Q = \{1, 2, 3\}\) and \(S = \{2, 3, 1\}\) are equal.
Q18
The set \(P = \{x | x \in Z, x \text{ is a multiple of } 3\}\) is a subset of \(T = \{x | x \in Z, x \text{ is a multiple of } 6\}\).
Q19
Given \(A = \{0, 1, 2\}\), \(B = \{x \in R | 0 \le x \le 2\}\). Then \(A = B\).

True or False (20-24)

Q20
For all sets \(A\) and \(B\), \((A - B) \cup (A \cap B) = A\).
Q21
For all sets \(A, B\) and \(C\), \(A - (B - C) = (A - B) - C\).
Q22
For all sets \(A, B\) and \(C\), if \(A \subset B\), then \(A \cap C \subset B \cap C\).
Q23
For all sets \(A, B\) and \(C\), if \(A \subset B\), then \(A \cup C \subset B \cup C\).
Q24
For all sets \(A, B\) and \(C\), if \(A \subset C\) and \(B \subset C\), then \(A \cup B \subset C\).

Short Answer Type Questions (25-29)

Q25
For all sets \(A\) and \(B\), prove that \(A \cup (B - A) = A \cup B\).
Q26
For all sets \(A\) and \(B\), prove that \(A - (A - B) = A \cap B\).
Q27
For all sets \(A\) and \(B\), prove that \(A - (A \cap B) = A - B\).
Q28
For all sets \(A\) and \(B\), prove that \((A \cup B) - B = A - B\).
Q29
Let \(T = \{x | \frac{x+5}{x-7} - 5 = \frac{4x-40}{13-x}\}\). Is \(T\) an empty set? Justify your answer.
← Exercise 1.1 Exercise 1.3 →