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Q5(ii):
Are the following pair of sets equal ? Give reasons. (ii) $A = \{ x : x$ is a letter in the word FOLLOW\} $B = \{ y : y$ is a letter in the word WOLF\}
Solution :
Step 1: Roster Form Representation of Set A
Given set $A = \{ x : x \text{ is a letter in the word FOLLOW} \}$. To represent set $A$ in roster form, we list the distinct elements of the word "FOLLOW". By the definition of a set, each element must be unique [Per the Principle of Extensionality, a set is determined solely by its members].
- Letters in "FOLLOW": F, O, L, L, O, W.
- Distinct letters: F, O, L, W.
Thus, $A = \{F, O, L, W\}$.
Step 2: Roster Form Representation of Set B
Given set $B = \{ y : y \text{ is a letter in the word WOLF} \}$. To represent set $B$ in roster form, we list the distinct elements of the word "WOLF".
- Letters in "WOLF": W, O, L, F.
- Distinct letters: W, O, L, F.
Thus, $B = \{W, O, L, F\}$.
Step 3: Analytical Comparison
Two sets are considered equal if and only if they contain the exact same elements, regardless of the order in which they are written [Per the Axiom of Equality for Sets: $A = B \iff (\forall x, x \in A \implies x \in B) \land (\forall y, y \in B \implies y \in A)$].
| Set | Elements |
|---|---|
| $A$ | $\{F, O, L, W\}$ |
| $B$ | $\{W, O, L, F\}$ |
Comparing the sets:
- Every element in $A$ is present in $B$.
- Every element in $B$ is present in $A$.
- The cardinality of both sets is identical: $n(A) = 4$ and $n(B) = 4$.
Step 4: Visual Representation
Final Solution: Yes, the sets A and B are equal because they contain the exact same elements $\{F, O, L, W\} = \{W, O, L, F\}$.
More Questions from Class 11 Mathematics Sets EXERCISE 1.2
- Q1(i): Which of the following are examples of the null set (i) Set of odd natural numbers divisible by 2
- Q1(ii): Which of the following are examples of the null set (ii) Set of even prime numbers
- Q1(iii): Which of the following are examples of the null set (iii) \{ $x$ : $x$ is a natural numbers, $x < 5$ and $x > 7$ \}
- Q1(iv): Which of the following are examples of the null set (iv) \{ $y$ : $y$ is a point common to any two parallel lines\}
- Q2(i): Which of the following sets are finite or infinite (i) The set of months of a year
- Q2(ii): Which of the following sets are finite or infinite (ii) \{1, 2, 3, . . .\}
- Q2(iii): Which of the following sets are finite or infinite (iii) \{1, 2, 3, . . .99, 100\}
- Q2(iv): Which of the following sets are finite or infinite (iv) The set of positive integers greater than 100
- Q2(v): Which of the following sets are finite or infinite (v) The set of prime numbers less than 99
- Q3(i): State whether each of the following set is finite or infinite: (i) The set of lines which are parallel to the x-axis
- Q3(ii): State whether each of the following set is finite or infinite: (ii) The set of letters in the English alphabet
- Q3(iii): State whether each of the following set is finite or infinite: (iii) The set of numbers which are multiple of 5
- Q3(iv): State whether each of the following set is finite or infinite: (iv) The set of animals living on the earth
- Q3(v): State whether each of the following set is finite or infinite: (v) The set of circles passing through the origin (0,0)
- Q4(i): In the following, state whether $A = B$ or not: (i) $A = \{ a, b, c, d \}$ $B = \{ d, c, b, a \}$
- Q4(ii): In the following, state whether $A = B$ or not: (ii) $A = \{ 4, 8, 12, 16 \}$ $B = \{ 8, 4, 16, 18\}$
- Q4(iii): In the following, state whether $A = B$ or not: (iii) $A = \{2, 4, 6, 8, 10\}$ $B = \{ x : x$ is positive even integer and $x \le 10\}$
- Q4(iv): In the following, state whether $A = B$ or not: (iv) $A = \{ x : x$ is a multiple of 10\}, $B = \{ 10, 15, 20, 25, 30, . . . \}$
- Q5(i): Are the following pair of sets equal ? Give reasons. (i) $A = \{2, 3\}$, $B = \{x : x$ is solution of $x^2 + 5x + 6 = 0\}$
- Q6: From the sets given below, select equal sets : $A = \{ 2, 4, 8, 12\}$, $B = \{ 1, 2, 3, 4\}$, $C = \{ 4, 8, 12, 14\}$, $D = \{ 3, 1, 4, 2\}$ $E = \{–1, 1\}$, $F = \{ 0, a\}$, $G = \{1, –1\}$, $H = \{ 0, 1\}$
CBSE Solutions for Class 11 Mathematics Sets
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