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An element x is in set A only if it is in set B . M. Chen ([email protected]) ENGG2430 lecture 1 12 / 16 De Morgan’s laws Two particularly useful properties are given by De Morgan’s laws
which state that
c
(∪n Sn )c = n Sn ,
c = ∪ Sc
( n Sn )
nn Proof of (∪n Sn )c = c
n Sn (one way) Suppose that x ∈ (∪n Sn )c .Then, x ∈ ∪n Sn , which implies that for
/
every n, we have x ∈ Sn .
/
c
Thus, x belongs to the complement of every Sn , and x ∈ n Sn . M. Chen ([email protected]) ENGG2430 lecture 1 13 / 16 Venn diagrams of De Morgan’s laws when n=2 (A B )c Ac Bc M. Chen ([email protected]) ENGG2430 lecture 1 14 / 16 Exercise
Let A = {set of all persons taller than 1.6 meters}, B = {set of all persons
heavier than 60kg}, C = {set of all persons who wear glasses}.
What is the set of all persons who are shorter than 1.6 meters or wear
glasses?
What is the set of all persons who are taller than 1.6 meters and are
heavier than 60kg, but do not wear glasses?
Express these statements in terms of A, B , and C :
There is no one who wears glasses and is shorter than 1.6 meters.
If a person is lighter than 60kg, then he/she must either wear glasses or
is taller than 1.6 meters. Can you relate:
A ∪ B and A ∩ B ?
A ∪ B and Ac ∩ B c ? If A ⊂ B , what can you say about the relationship between Ac and
Bc ?
M. Chen ([email protected]) ENGG2430 lecture 1 15 / 16 Thank You Reading: Ch. 1.1 and 1.2 of the textbook M. Chen ([email protected]) ENGG2430 lecture 1 16 / 16...
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This document was uploaded on 03/31/2014.
 Spring '14

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