Question 1: If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, write the set notation for A ∩ B and A ∪ B.

Answer: A ∩ B = {3, 4}; A ∪ B = {1, 2, 3, 4, 5, 6}

Question 2: Given sets C = {x | x is an even number less than 10} and D = {2, 4, 6, 8}, express C in set notation.

Answer: C = {x | x is an even number less than 10}

Question 3: Construct the Venn diagram on the grid representing sets E = {1, 2, 3, 4} and F = {3, 4, 5, 6}. Shade the region representing E ∩ F.

Answer: (student draws the intersection of E and F)

Question 4: Calculate |E ∪ F| given the sets from the previous question.

Answer: 4

Question 5: A class of 40 students has 25 who like basketball, 18 who like football, and 10 who like both. How many students like neither sport? Use set notation in your explanation.

Answer: Students liking either sport = B ∪ F = 25 + 18 - 10 = 33; Neither = 40 - 33 = 7

Question 6: Express the complement of set G = {2, 4, 6, 8} relative to the universal set {1, 2, 3, 4, 5, 6, 7, 8} in set notation.

Answer: G' = {x | x ∈ {1,2,3,4,5,6,7,8} and x ∉ G} = {1,3,5,7}

Question 7: Given sets H = {a, b, c} and I = {b, c, d}, find H ∆ I (symmetric difference) and explain what it represents in set notation.

Answer: H ∆ I = {a, d}; elements in either H or I but not in both

Question 8: Construct a Venn diagram on the grid for sets M = {1, 2, 3, 4} and N = {3, 4, 5, 6}. Shade the region representing (M ∪ N)'.

Answer: (student shades the outside region of union M ∪ N)

Question 9: If set J = {x | x is a multiple of 3 less than 12} and set K = {3, 6, 9}, find J extbackslash K and describe it in set notation.

Answer: J ackslash K = {x | x is a multiple of 3 less than 12 and x ∉ K} = {3, 6, 9} ackslash {3, 6, 9} = ∅

Question 10: Identify and correct the mistake in this set notation: {x | x is an odd number less than 5} = {1, 2, 3, 4}.

Answer: Incorrect; the set of odd numbers less than 5 is {1, 3}

Question 11: Challenge: Given sets P = {1, 2, 3, 4, 5} and Q = {4, 5, 6, 7}, find (P ∩ Q)′ and explain its meaning in set notation.

Answer: (P ∩ Q)′ = {x | x ∈ universal set and x ∉ {4, 5}}