Exercise 1A - Further Sets

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Exercise 2a

Overview

Exercise 1A from New Syllabus Mathematics Book 4 (8th Edition) offers students an in-depth opportunity to practice the fundamentals of set theory and Venn diagrams. Covering union, intersection, and subsets through both symbolic notation and diagrammatic representation, this exercise develops logical thinking and visualization skills across 15 questions of varying difficulty levels: Basic, Intermediate, and Advanced.

List of Questions in Exercise 1A

  1. It is given that A = {1, 2, 3, 4, 7} and B = {2, 4, 8, 10}.
    (i) List all the elements of A ∩ B in set notation.
    (ii) Draw a Venn diagram to represent the sets A and B.
  2. It is given that C = {blue, green, yellow, orange, red, pink} and D = {yellow, pink, blue}.
    (i) List all the elements of C ∩ D in set notation.
    (ii) Draw a Venn diagram to represent the sets C and D.
  3. It is given that E = {p, q, r} and F = {s, t}.
    (i) List all the elements of E ∩ F in set notation.
    (ii) Draw a Venn diagram to represent the sets E and F.
  4. It is given that G = {apple, orange, banana, grape, durian, pear} and H = {apple, banana, grape, strawberry}.
    (i) Draw a Venn diagram to represent the sets G and H.
    (ii) From the Venn diagram, list all the elements of G ∪ H in set notation.
  5. It is given that I = {w, y} and J = {v, w, x, y, z}.
    (i) Draw a Venn diagram to represent the sets I and J.
    (ii) From the Venn diagram, list all the elements of I ∪ J in set notation.
  6. It is given that K = {11, 13, 19, 21} and L = {12, 14, 15, 16, 17, 18, 20}.
    (i) Draw a Venn diagram to represent the sets K and L.
    (ii) From the Venn diagram, list all the elements of K ∪ L in set notation.
  7. It is given that M = {x : x is a perfect square such that 0 < x < 70} and N = {x : x is a perfect cube such that 0 < x < 70}.
    (i) List all the elements of M and N in set notation.
    (ii) Find M ∩ N.
    (iii) Draw a Venn diagram to represent the sets M and N.
  8. It is given that P = {x : x is a multiple of 8 such that 0 < x ≤ 32} and Q = {x : x is a multiple of 4 such that 0 < x ≤ 32}.
    (i) List all the elements of P and Q in set notation.
    (ii) Find P ∩ Q.
    (iii) Draw a Venn diagram to represent the sets P and Q.
    (iv) Is P ∩ Q = P? Explain.
  9. It is given that R = {x : x is a positive integer and a factor of 18} and S = {x : x is a composite number between 9 and 18}.
    (i) List all the elements of R and S in set notation.
    (ii) Find R ∩ S. Explain.
    (iii) Draw a Venn diagram to represent the sets R and S.
  10. It is given that T = {x : x is a multiple of 3 such that 0 < x ≤ 18} and V = {x : x is a positive integer and a factor of 18}.
    (i) List all the elements of T and V in set notation.
    (ii) Draw a Venn diagram to represent the sets T and V.
    (iii) Find T ∪ V.
  11. It is given that W = {x : x is a multiple of 4 such that 1 ≤ x < 16} and X = {x : x is a positive integer and a factor of 24}.
    (i) List all the elements of W and X in set notation.
    (ii) Draw a Venn diagram to represent the sets W and X.
    (iii) From the Venn diagram, find W ∪ X.
    (iv) Is W ∪ X = X? Explain.
  12. It is given that Y = {x : x is a positive integer and a factor of 25} and Z = {x : x is a multiple of 6 such that 0 < x < 25}.
    (i) List all the elements of Y and Z in set notation.
    (ii) Draw a Venn diagram to represent the sets Y and Z.
    (iii) From the Venn diagram, find Y ∪ Z.
  13. It is given that A = {(x, y) : (x, y) are coordinates of a point on the curve y = x² – 3x + 2 such that x and y are integers} and B = {(x, y) : (x, y) are coordinates of a point on the line y = 0 such that x and y are integers}.
    Describe A ∩ B in set notation.
  14. It is given that C = {(x, y) : (x, y) lies on the curve y = x² + x + 2} and D = {(x, y) : (x, y) lies on the line y = 3x + 5}.
    List all the elements of C ∩ D in set notation.
  15. It is given that E = {y : y is the y-coordinate of a point on the curve y = (x – 5)² + 3} and F = {y : y is the y-coordinate of a point on the curve y = (x + 2)² – 4}.
    Describe E ∪ F in set notation.

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