More set opertations: Philosophy Forums

More set opertations

Christim
Aspirant

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Posted 10/02/09 - 11:47 AM: Subject: More set opertations	#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:	#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
Student

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Posted 10/02/09 - 07:32 PM:	#3
Everything is correct except 3(b), for which the answer is A(k) = {...-3,-2,-1,0,...,k}

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