Question 1: If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6}, find A ∪ B (the union of A and B).

Answer: A ∪ B = {1, 2, 3, 4, 5, 6}

Question 2: Given set C = {x | x is an even number less than 10}, write C in set-builder notation.

Answer: C = {x | x is an even number and x < 10}

Question 3: If set D = {1, 3, 5, 7} and set E = {3, 4, 5, 6}, what is D ∩ E?

Answer: D ∩ E = {3, 5}

Question 4: Construct a Venn diagram illustrating the sets F = {2, 4, 6} and G = {4, 5, 6, 7}. Label the regions accordingly.

Answer: Students will draw the diagram; check for correct overlaps and labeling.

Question 5: Calculate the complement of set H = {1, 2, 3} within the universal set U = {1, 2, 3, 4, 5, 6}.

Answer: H' = {4, 5, 6}

Question 6: If 60% of students like basketball and 40% like football, and 10% like both, what is the percentage of students who like either sport?

Answer: P(B ∪ F) = 60% + 40% - 10% = 90%

Question 7: Express the set containing all natural numbers less than 5 using set notation.

Answer: {x | x is a natural number and x < 5}

Question 8: A survey shows 70 students play tennis, 50 play basketball, and 20 play both. How many students play neither sport if the total surveyed is 120?

Answer: Number playing neither = 120 - (70 + 50 - 20) = 120 - 100 = 20

Question 9: Given sets J = {a, b, c} and K = {b, c, d}, find the set difference J - K.

Answer: J - K = {a}

Question 10: Identify the error in the following statement: 'The intersection of sets P and Q is the set of elements in P or Q.'

Answer: Error: The intersection is the set of elements in both P and Q, not in either.

Question 11: Construct a set that contains all integers from 1 to 10 that are multiples of 3.

Answer: {3, 6, 9}

Question 12: If set R = {x | x is a real number between 0 and 1} and set S = {x | x is rational between 0 and 1}, write the set notation for irrational numbers in R.

Answer: R \\ S