COSI 155b Chapter Notes - Chapter 4: Symmetric Difference
5 Jun 2018
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Set Operations
Set Operations and Venn Diagrams
Every set A exists within some universe u.
The complement of A is written as Ac .
The elements in set Ac is any element in the universe u that is not an element of A.
If A = {a,b,c} and u = {a,b,c,d,e,f}, then Ac = {d,e,f}.
Intersections
Given sets A and B, the intersection of A and B is A .
Unions
Given sets A and B, the union of A and B is A .
Difference between Sets
Given sets A and B, the difference, A-B, is defined as A-B = {x|x is an element of A and not an
element of B}.
A-B is also written as A\B.
Intervals
The brackets [] are inclusive.
If A = [0,2] and B = [1,6), then:
• A = [1,2]
• AUB = [0,6)
• B-A = (2,6)
• AC = (-infinity, 0) U (2, infinity)
Symmetric Difference
Ais the symmetric difference of A and B ( .
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Document Summary
Every set a exists within some universe u. The complement of a is written as ac . The elements in set ac is any element in the universe u that is not an element of a. If a = {a,b,c} and u = {a,b,c,d,e,f}, then ac = {d,e,f}. Given sets a and b, the intersection of a and b is a(cid:1514)(cid:1828)={ (cid:1827) (cid:1866)(cid:1856) (cid:1828)}. Given sets a and b, the union of a and b is a(cid:1515)(cid:1828)={| (cid:1827) (cid:1867)(cid:1870) (cid:1828)}. Given sets a and b, the difference, a-b, is defined as a-b = {x|x is an element of a and not an element of b}. If a = [0,2] and b = [1,6), then: a(cid:1514)(cid:1828) = [1,2, aub = [0,6, b-a = (2,6, ac = (-infinity, 0) u (2, infinity) A (cid:1828) is the symmetric difference of a and b ( (cid:1827) (cid:1828)(cid:4667).
