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Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}.
\n" ); document.write( "To start with
- I am going to assume that U = {All the lowercase letters of the alphabet}. If this is incorrect, then the answers to (c), (d) and (e) will be incomplete.
- To avoid any potential confusion, I will use U for the \"universal\" set and \"u\" for the union operator
- When the elements of a set are listed, the order is not important
- The union operator, u, is an inclusive operator. The union of two sets will always include every member of both sets. Elements of both sets, if any, are listed only once in the union. (Never list duplicate elements in any set.)
- The intersection operator, ∩, is an exclusive operator. The intersection of two sets will include only elements that are members of both sets.
\n" ); document.write( "(a) A u B
\n" ); document.write( "This means \"the set whose elements are members of set A or set B (or both)\".
\n" ); document.write( "A u B = {c, d, e, f, g, h, k}
\n" ); document.write( "(b) A ∩ B
\n" ); document.write( "This means \"the set whose elements are members of both set A and set B\".
\n" ); document.write( "A ∩ B = {e, f}
\n" ); document.write( "(c) A′ ∩ B′
\n" ); document.write( "A′ means \"the set of all elements of the universal set, U, which are not members of set A.
\n" ); document.write( "A′ = {a, b, g, h, i, j, k, l, m, ..., z}
\n" ); document.write( "B′ means \"the set of all elements of the universal set, U, which are not members of set B.
\n" ); document.write( "B′ = {a, b, c, d, i, j, l, m, ..., z}
\n" ); document.write( "A′ ∩ B′ means \"the set whose elements are members of both set A' and set B'\".
\n" ); document.write( "A′ ∩ B′ = {a, b, i, j, l, m, ..., z}
\n" ); document.write( "(d) A′ u B′
\n" ); document.write( "This means \"the set whose elements are members of set A′ or set B′ (or both)\". Using A′ and B′ from (c) we get
\n" ); document.write( "A′ u B′ = {a, b, c, d, g, h, i, j, k, l, m, ..., z}
\n" ); document.write( "(e) A u B′
\n" ); document.write( "This means \"the set whose elements are members of set A or set B′ (or both)\". Using A and B′ from (c) we get
\n" ); document.write( "A u B′ = {a, b, c, d, e, f, i, j, l, m, ..., z}
\n" ); document.write( "(f) (A u B′) ∩ B
\n" ); document.write( "The first part of this is the answer to part (e). (A u B′) ∩ B means \"the set whose elements are members of the set B and members of the answer to part (e)\"
\n" ); document.write( "(A u B′) ∩ B = {e, f}
\n" ); document.write( "(g) (A u B) ∩ (A u B′)
\n" ); document.write( "The first part is the answer to part (a), The last part is the answer to part (e). So (A u B) ∩ (A u B′) means \"the set whose members are members of the answer to part (a) and members to the answer to part (e)\". So
\n" ); document.write( "(A u B) ∩ (A u B′) = {c, d, e, f} (which is set A}
\n" ); document.write( " \n" ); document.write( "