Set Theory Cardinality Quiz

Set Operations and Relations

Problem 1

• If n(A× B) = 6 and A = {1, 3} then n(B) can be found using the formula n(A× B) = n(A) × n(B)
• We know n(A) = 2, so n(B) = n(A× B) / n(A) = 6 / 2 = 3

Problem 2

• A = {a,b, p}, B = {2, 3}, C = {p,q,r,s}
• We need to find n[(A ∪ C )× B]
• First, find A ∪ C = {a,b,p,q,r,s}
• Then, find (A ∪ C )× B = {(a,2),(a,3),(b,2),(b,3),(p,2),(p,3),(q,2),(q,3),(r,2),(r,3),(s,2),(s,3)}
• So, n[(A ∪ C )× B] = 12

Problem 3

• A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}, D = {5, 6, 7, 8}
• We need to find which statement is true
• Statements can include A ∪ B, A ∩ B, B - A, etc.
• We need to evaluate each statement to find the true one

Problem 4

• There are 1024 relations from A = {1, 2, 3, 4, 5} to a set B
• We know the number of relations is n(A) × n(B) = 1024
• Since n(A) = 5, we can find n(B) = 1024 / 5 = 2048 / 5 = 32

Test your knowledge of set theory by determining the cardinality of set B when the cardinality of the Cartesian product of sets A and B is given. In this case, A = {1, 3} and n(A× B) = 6.