Let \(A = \{2, 4, 6, \ldots, 20\}\), \(B = \{3, 6, 9, \ldots, 30\}\), then the number of elements in \(A - B\) are ____.
7
A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} has 10 elements.
B = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}.
Common elements: \(A \cap B = \{6, 12, 18\}\), i.e. 3 elements.
\(A - B = \{2, 4, 8, 10, 14, 16, 20\}\), so \(n(A - B) = 10 - 3 = 7\).
Hence, the answer is 7.
Similar Questions
Choose the true statement representing union distributing over intersection.
Important Questions from Operations on Sets
Let R be a relation on a set A such that R = R-1, then R is
In a beauty contest, half the number of experts voted for Mr. A and two third voted for Mr. B. 10 voted for both and 6 did not for either. How many experts were there in all?
In a survey where 100 students reported which subjects they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business, 8 students liked both Business and Literature, 5 students liked all three subjects.
Then the number of people who liked exactly one subject is
A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics: n(P) = 8, n(Q) = 13, n(R) = 13, n(P ∩ R) = 3, n(P ∩ R) = 3, n(Q ∩ R) = 3, n(Q ∩ R) = 6, n(P ∩ Q ∩ R) = 2, where n(x) is the cardinality of the set x. Then the number of text books that have no material on compilers is
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 3, 4,}
B = {2, 4, 6, 8), then (A ∪ B)' is -
