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Exercises to Sets

Q1. Let A = {1,2,3,4} and B = {3,4,5,6}. Find:

  • A ∪ B
  • A ∩ B
  • A − B
  • B − A
Reveal solution

Given:
A={1,2,3,4}A = \{1, 2, 3, 4\}
B={3,4,5,6}B = \{3, 4, 5, 6\}

Solutions:

  • A ∪ B (Union):
    Combine all elements from both sets, without repetition.
    A∪B={1,2,3,4,5,6}A ∪ B = \{1, 2, 3, 4, 5, 6\}

  • A ∩ B (Intersection):
    Elements common to both sets.
    A∩B={3,4}A ∩ B = \{3, 4\}

  • A − B (Difference):
    Elements in A that are not in B.
    A−B={1,2}A − B = \{1, 2\}

  • B − A (Difference):
    Elements in B that are not in A.
    B−A={5,6}B − A = \{5, 6\}

Q2. Find the cardinality of:

  • A = {letters in “KATHMANDU”}
  • B = {multiples of 5 ≤ 50}
Reveal solution

A = {letters in “KATHMANDU”}

List the distinct letters in "KATHMANDU":
K, A, T, H, M, N, D, U
There are 8 distinct letters.

Cardinality of A: n(A)=8n(A) = 8

B = {multiples of 5 ≤ 50}

List the multiples of 5 up to 50: {5, 10, 15, 20, 25, 30, 35, 40, 45, 50}
There are 10 such numbers.

Cardinality of B: n(B)=10n(B) = 10