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CBSE Class 11 (Commerce) Sets and Relations — practice questions — page 3

Explore 79 free Sets and Relations questions in CBSE Class 11 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets and Relations questions and exercises with answers

Showing questions 61–79 of 79.

If every element of A is in B and every element of B is in A, thenRead the answer and worked solution →Let A = {1}, B = {{1}, 2}, C = {{1}, 2, 3}. ThenRead the answer and worked solution →Which chain of inclusions among number sets is correct?Read the answer and worked solution →The set of all real numbers that are not rational is called the set ofRead the answer and worked solution →The set {x : a <= x < b} is written as the intervalRead the answer and worked solution →What is the length of the interval (-5, 7]?Read the answer and worked solution →Venn diagrams are named after which English logician?Read the answer and worked solution →Hockey: Ram, Geeta, Akbar. Football: Geeta, David, Ashok. How many play at least one?Read the answer and worked solution →If B is a subset of A, then A ∪ B equalsRead the answer and worked solution →Find the intersection of {2, 4, 6, 8} and {6, 8, 10, 12}.Read the answer and worked solution →If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}, find B - A.Read the answer and worked solution →If V = {a, e, i, o, u} and B = {a, i, k, u}, find V - B.Read the answer and worked solution →The sets A - B, A ∩ B and B - A are alwaysRead the answer and worked solution →U is all students of a mixed class and A is all its girls. What is A'?Read the answer and worked solution →For any subset A of U, the complement of A' isRead the answer and worked solution →By De Morgan's law, (A ∪ B)' is equal toRead the answer and worked solution →Within a universal set U, the complement of the empty set isRead the answer and worked solution →In which year did Bertrand Russell show that a set of all sets leads to a contradiction?Read the answer and worked solution →Who published the first axiomatisation of set theory in 1908?Read the answer and worked solution →

Worked practice questions

If every element of A is in B and every element of B is in A, then

  1. A and B are disjoint sets
  2. B is a proper subset of A
  3. A and B are equal sets
  4. A is a proper subset of B
Show answer and solution

Correct answer: C. A and B are equal sets

Mutual containment means both sets hold exactly the same elements, so they are equal.

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Let A = {1}, B = {{1}, 2}, C = {{1}, 2, 3}. Then

  1. A ⊂ C and A ∉ B
  2. A ⊂ B and A ⊂ C
  3. A ∈ B but A ⊄ C
  4. A = B and A ∈ C
Show answer and solution

Correct answer: C. A ∈ B but A ⊄ C

The set {1} is an element of B, and B is inside C, yet 1 itself is not in C, so A is not a subset of C.

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Which chain of inclusions among number sets is correct?

  1. Z ⊂ N ⊂ Q
  2. R ⊂ Q ⊂ Z
  3. Q ⊂ Z ⊂ N
  4. N ⊂ Z ⊂ Q
Show answer and solution

Correct answer: D. N ⊂ Z ⊂ Q

Every natural number is an integer and every integer is a rational number.

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More Mathematics topics

Straight Lines and Conic SectionsTrigonometric FunctionsStatistics and ProbabilityComplex Numbers and Quadratic EquationsLimits and DerivativesSequences and SeriesBinomial TheoremPermutations and Combinations