Questions and Answers
Find the power set of set A = { 1, 2, 3 } and the number of subsets of A.
The power set of set A, denoted by P(A), is the set of all subsets of A. The power set of A is given by P(A) = { {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} }. So, the number of subsets of A, denoted by n(A), is 8.
Calculate the symmetric difference between sets P = { 2, 3, 5, 6, 11 } and Q = { 1, 3, 5, 11 }.
The symmetric difference between sets P and Q, denoted by P Δ Q, is the set of elements that are in P or Q but not in both. The symmetric difference P Δ Q is given by P Δ Q = {1, 2, 6}.
Verify De Morgan’s laws for set difference using the sets A = { -2, 0, 1, 3, 5 }, B = { -1, 0, 2, 5, 6 }, and C = { -1, 2, 5, 6, 7 }.
De Morgan’s laws for set difference state that (A - B) U (A - C) = A - (B ∩ C) and (A ∩ B) - C = (A - C) ∪ (B - C). By using the given sets, we can verify these laws to be true.
Verify De Morgan’s laws of set complementation using the sets U = { 4, 7, 8, 10, 11, 12, 15, 16 }, A = { 7, 8, 11, 12 }, and B = { 4, 8, 12, 15 }.
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Find the number of students who speak all three languages among 100 students, given the language statistics.
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