RBSE Class 11 Maths: Chapter 1 (Sets) – Exercise 1.2 Solutions

Based on the official curriculum for the Rajasthan Board of Secondary Education (RBSE), the Class 11 Maths syllabus is aligned with the NCERT textbook. Therefore, the solutions for RBSE Class 11 Maths Chapter 1, Exercise 1.2 are the same as those for the NCERT curriculum.

This exercise focuses on the different types of sets, including null sets, finite and infinite sets, and equal sets.

Here are the step-by-step solutions for RBSE Class 11 Maths, Chapter 1 (Sets), Exercise 1.2.

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RBSE Class 11 Maths: Chapter 1 (Sets) – Exercise 1.2 Solutions

Question 1: Which of the following are examples of the null set?

i. Set of odd natural numbers divisible by 2.

• Solution: This is a null set. An odd natural number cannot be divisible by 2. Therefore, this set has no elements.

ii. Set of even prime numbers.

• Solution: This is not a null set. The number 2 is an even number and also a prime number. Therefore, the set contains one element: {2}.

iii. {x : x is a natural number, x < 5 and x > 7}

• Solution: This is a null set. No natural number can be both less than 5 and greater than 7 at the same time.

iv. {y : y is a point common to any two parallel lines}

• Solution: This is a null set. Parallel lines, by definition, never intersect. Therefore, they have no common points.

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Question 2: Which of the following sets are finite or infinite?

i. The set of months of a year.

• Solution: This is a finite set. The set has a definite number of elements, specifically 12.

ii. {1, 2, 3, ...}

• Solution: This is an infinite set. The ellipsis (…) indicates that the set of natural numbers continues indefinitely, so it has an infinite number of elements.

iii. {1, 2, 3, ..., 99, 100}

• Solution: This is a finite set. The set has a definite number of elements, from 1 to 100.

iv. The set of positive integers greater than 100.

• Solution: This is an infinite set. The positive integers greater than 100 (101, 102, 103, …) continue indefinitely.

v. The set of prime numbers less than 99.

• Solution: This is a finite set. There is a definite number of prime numbers less than 99, even though the list is long. For example, {2, 3, 5, 7, …, 97}.

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Question 3: State whether each of the following sets is finite or infinite.

i. The set of lines which are parallel to the x-axis.

• Solution: This is an infinite set. An infinite number of lines can be drawn parallel to the x-axis.

ii. The set of letters in the English alphabet.

• Solution: This is a finite set. The English alphabet contains a definite number of letters, 26.

iii. The set of numbers which are multiple of 5.

• Solution: This is an infinite set. The multiples of 5 (5, 10, 15, …) continue indefinitely.

iv. The set of animals living on the earth.

• Solution: This is a finite set. While the number is extremely large and constantly changing, it is a definite number at any given point in time. It is not infinite.

v. The set of circles passing through the origin (0, 0).

• Solution: This is an infinite set. An infinite number of circles, each with a different center and radius, can pass through a single point (the origin).

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Question 4: In the following, state whether A = B or not.

i. A = {a, b, c, d} ; B = {d, c, b, a}

• Solution: A = B. The order in which elements are listed in a set does not matter. Since both sets have the exact same elements, they are equal.

ii. A = {4, 8, 12, 16} ; B = {8, 4, 16, 18}

• Solution: A ≠ B. While they share some elements, the element 12 is in set A but not in set B, and the element 18 is in set B but not in set A. For sets to be equal, they must have exactly the same elements.

iii. A = {2, 4, 6, 8, 10} ; B = {x : x is a positive even integer and x ≤ 10}

• Solution: A = B. When we write set B in roster form, it becomes {2, 4, 6, 8, 10}. Both sets contain the exact same elements.

iv. A = {x : x is a multiple of 10} ; B = {10, 15, 20, 25, 30, ...}

• Solution: A ≠ B. Set A contains multiples of 10: {10, 20, 30, 40, ...}. Set B contains 15 and 25, which are not multiples of 10. Therefore, the sets are not equal.

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Question 5: Are the following pairs of sets equal? Give reasons.

i. A = {2, 3} ; B = {x : x is a solution of x² + 5x + 6 = 0}

• Solution: First, solve the quadratic equation to find the elements of set B.
  • x2+5x+6=0
  • x2+3x+2x+6=0
  • x(x+3)+2(x+3)=0
  • (x+2)(x+3)=0
  • So, x=−2 or x=−3.
• The elements of set B are {−2,−3}.
• Conclusion: A ≠ B because the elements of the sets are different.

ii. A = {x : x is a letter in the word FOLLOW} ; B = {y : y is a letter in the word WOLF}

• Solution: First, write both sets in roster form, listing only the unique elements.
  • A = {F, O, L, W}
  • B = {W, O, L, F}
• Conclusion: A = B because both sets have the exact same elements, even though the order is different.

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Question 6: 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}
• Solution: Compare the elements of each set to find the pairs that are exactly identical.
  • Set B = {1, 2, 3, 4} and Set D = {3, 1, 4, 2}. Both sets contain the same elements.
  • Set E = {-1, 1} and Set G = {1, -1}. Both sets contain the same elements.
• Conclusion: The pairs of equal sets are:
  • B = D
  • E = G