Introduction to Math Proof

Mathematics
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Question 1:Let U={1,3,...,15} be the universal set. A={1,5,9,13}, and B={3,9,15}. Determine the following:

(a). A U B,        (b). A ∩ B,         (c). A\B,          (d). B\A,         (e). A^c,          (f). A U B^c

Mar 15th, 2015

a) A U B = {1, 3, 5, 9, 13, 15} includes all elements belonging at least to one of the sets A or B,

b)  A ∩ B = {9} includes the elements belonging to both sets A and B,

c) A \ B = {1, 5, 13} includes the elements of A that do not belong to B,

d) B \ A = {3, 15} includes the elements of B that do not belong to A,

e) A^c = U \ A = {3, 7, 11, 15} - the complement of A includes all elements of U that do not belong to A

f) A U B^c = {1, 5, 9, 13} U {1, 5, 7, 11, 13} = {1, 5, 7, 9, 11, 13}  - first find the complement to B, then take the union of A and B^c.

Mar 15th, 2015

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