Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e. #(XUY)+#(XnY) = #(X)+#(Y), where, for sets S and T, • #(S) denotes the size of S SUT denotes the union of S and T, i.e. and SUT = {u E Ulu S or u € T}, T denotes the intersection of S and Tie (4) (5)
Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e. #(XUY)+#(XnY) = #(X)+#(Y), where, for sets S and T, • #(S) denotes the size of S SUT denotes the union of S and T, i.e. and SUT = {u E Ulu S or u € T}, T denotes the intersection of S and Tie (4) (5)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:6 which may be ∞, in which case, the above equality should be appropriately considered...
where U is some universe in which S and T live, i.e. U is a set and S C U and T C U.
![An all-inclusive, yet exclusive club.
Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e.
#(XUY)+#(XnY)=#(X)+#(Y),
where, for sets S and T,
• #(S) denotes the size of S,
SUT denotes the union of S and T, i.e.
SUT = {u € U│u € S or u € T},
and
SnT denotes the intersection of S and T, i.e.
SnT :=
{u € U]u € S and u € T}]
(4)
(5)
(6)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1797707a-0d96-41d6-8f45-19c20e886f5b%2F1cef9995-bb3b-4f42-b6ea-0f839a492939%2F4fr67v_processed.png&w=3840&q=75)
Transcribed Image Text:An all-inclusive, yet exclusive club.
Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e.
#(XUY)+#(XnY)=#(X)+#(Y),
where, for sets S and T,
• #(S) denotes the size of S,
SUT denotes the union of S and T, i.e.
SUT = {u € U│u € S or u € T},
and
SnT denotes the intersection of S and T, i.e.
SnT :=
{u € U]u € S and u € T}]
(4)
(5)
(6)
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