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More set opertations
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More set opertations
Christim
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Posted 10/02/09 - 11:47 AM:
Subject: More set opertations
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#1
1) Express the following sets by listing the elements explicitly
within braces, separated by commas:

a) {x | x = x^2}
(we use "^" to indicate an exponent; x^2 means x squared)

{ 0,1} since (1 = 1^2 an 0 = 0^2)

b) {z | (-1 < z/3 < 1)} (assume the universe is integers)

{-2,-1,0,1,2}

c) {y | y MEMBER ({a,b,d,e} INTERSECT {0,1,2,c})}

Im not to sure about this one. I assume its { } ( emptyset) b/c (a,b,d,e) does not match (0,1,2,c)


2) What is the cardinality of

a) {{1,2,3,4,5,6,7,15,23,77,107,88}} 1


b) {EMPTYSET, {EMPTYSET}, {{EMPTYSET}}} 3

c) {0,{1,{2,{3,{4}}}}} 2

Im not too sure about all my answers .I know cardinality refers to number of elements, but how do I consider multiple elements within a subset.


3)Let set A(i) = {...-3,-2,-1,0,...,i}

a) Find UNION(i=k,INF) A(i)
i assumed this is all integers = Z

b) Find INTERSECT(i=k,INF) A(i)
A(k) = {k}

Can someone check if my answers are correct and help me with the probelms im haivng.

Timothy
Undead Mariachi
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Posted 10/02/09 - 12:02 PM:
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#2
They all seem ok, but I don't think I really understand the i=k, INF in 3). Also, in a) it says UNION, but I don't know between which sets it's operating. Same in b).

"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson
ClaudeHooper
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Posted 10/02/09 - 07:32 PM:
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#3
Everything is correct except 3(b), for which the answer is

A(k) = {...-3,-2,-1,0,...,k}
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