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Sets test

  1. Write the following sets in roster form:

    1. \(A = \{x : x \in N \,\text{and}\, x^2 < 8\}\)
    2. \(B = \{x : x \, \text{is a letter in the word EXAMINATION}\}\)
    3. \(C = \{x : x \, \text{is a prime number less than 15}\}\)

  2. Write the following sets in set builder form:

    1. \(A = \{ 1, 3, 5, 7, 9 \}\)
    2. \(B = \{ 9, 16, 25, 36, 49 \}\)
    3. \(C = \{ 1, 2, 3, 4, 6, 12 \}\) [Hint: These are factors of a number.]

  3. Find whether the following sets are equal:

    1. \(A = \{x: x \in N \,\text{and}\, x \leq 2\}\) and \(B=\{ x: x \,\text{is solution of}\, x^2-3x+2=0 \}\)
    2. \(C = \{x: x = 2n-1, n\in N \text{ and } n \leq 5\}\) and \(D=\{ x: x \text{ is an odd natural number less than 10} \}\)

  4. Consider the following sets: \(A = \{ 1, 2, 3, 4 \}\), \(B = \{x : x \text{ is a factor of 6}\}\) and \(C=\{ x: x \in N \text{ and } x \leq 3 \}\). Find which of the following sets are subsets of one another.

  5. Consider the following sets: \(A = \{ 2, 4, 6, 8 \}\), \(B = \{ 2, 3, 5, 7 \}\). Then find:

    1. \(A \cup B\)
    2. \(A \cap B\)
    3. \(A - B\)
    4. \(B - A\)

  6. Let \(U\) be the set of all triangles in a plane. If \(A\) is the set of all triangles with at least one angle different from \(90^\circ\), then what is \(A'\)?

  7. Find sets \(A\), \(B\) and \(C\) such that \(A\cap B\), \(B \cap C\) and \(A \cap C\) are non-empty sets and \(A \cap B \cap C = \phi\).