Discrete Mathematics University of Kentucky CS 275 Spring ... - MGNet

Definition: n sets A i are disjoint if A 1 3A 2 3…3A n = /.
Definition: The complement of set S with respect to T, denoted T4S, is defined
by T4S = {x,T | x6S}. T4S is also called the difference of S and T.
Definitions: The universal set is denoted U. The universal complement of S is
S = U4S.
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Examples:
• Let S = {1, 0} and T = {0, 1, 2}. Then
o S1T.
o S3T = S.
o S2T = T.
o T4S = {2}.
o Let U = N 0 . S = {2, 3, …}
• Let S = {0, 1} and T = {2, 3}. Then
o S5T.
o S3T = /.
o S2T = {0, 1, 2, 3}.
o T4S = {2, 3}.
o Let U=R. Then S is the set of all reals except the integers 0 and 1, i.e.,
S = {x,R | x-0 ! x-1}.
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