Maths · Sets, functions and groups. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A set is a well-defined collection of distinct objects. It can be written in descriptive form (in words), tabular form (elements listed in braces) or set-builder form, such as {x | x ∈ N ∧ x is even}.
A is a subset of B when every element of A is also in B. It is a proper subset when, in addition, A ≠ B. The empty set ∅ is a subset of every set.
Sets are combined by union, intersection, difference and complement, all taken inside a universal set U. The power set P(A) is the set of all subsets of A.
In De Morgan's laws students take the complement of each set but forget to change the sign. The complement of a union is the intersection of the complements, and the complement of an intersection is the union of the complements.
Answer: Both sides equal {7, 8}, so the law is verified.
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