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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 $x \le 10\}$
Solution :
Step 1: Analyzing Set A
Set $A$ is given in Roster Form as:
$A = \{2, 4, 6, 8, 10\}$
The elements of $A$ are clearly identified as the first five positive even integers.
Step 2: Analyzing Set B
Set $B$ is given in Set-Builder Form as:
$B = \{x : x \text{ is a positive even integer and } x \le 10\}$
To determine the contents of set $B$, we identify all positive even integers $x$ such that $x \le 10$.
The positive even integers are $2, 4, 6, 8, 10, 12, 14, \dots$
Applying the constraint $x \le 10$, we select the elements that satisfy this condition:
$B = \{2, 4, 6, 8, 10\}$
Step 3: Verification of Set Equality
Definition of equal sets: Two sets $A$ and $B$ are said to be equal if and only if every element of $A$ is an element of $B$, and every element of $B$ is an element of $A$ [Per the Axiom of Extensionality].
| Set | Elements |
|---|---|
| $A$ | $\{2, 4, 6, 8, 10\}$ |
| $B$ | $\{2, 4, 6, 8, 10\}$ |
Since all elements of $A$ are contained within $B$, and all elements of $B$ are contained within $A$, the sets are identical.
Final Solution: Yes, $A = B$ because both sets contain exactly the same elements $\{2, 4, 6, 8, 10\}$.
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(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 $x^2 + 5x + 6 = 0\}$
- 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\}
- 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
Chapters in CBSE - Class 11 Mathematics
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