# Thread: [SOLVED] discrete math help for B union E

1. ## [SOLVED] discrete math help for B union E

let U= {arithmetic, algebra, calculus, geometry, trigonometry, analysis, topology, statistics}

B= {analysis, topology, calculus}
E= {algebra, calculus, geometry, trigonometry, analysis}
in each of the following, represent the given set by an array of zeros and ones.

1) the complement of B union E

what i got was 1, 1, 0, 1, 1, 0, 0, 1 but it's wrong. i think the "complement of B" thing threw me off. any help would be greatly appreciated! i just started this course so the answer might be really easy but i don't get it XD also, is there a way to write "the complement of..." as a letter with a line over it? thanks =)

2. Originally Posted by e____o
let U= {arithmetic, algebra, calculus, geometry, trigonometry, analysis, topology, statistics}

B= {analysis, topology, calculus}
E= {algebra, calculus, geometry, trigonometry, analysis}
in each of the following, represent the given set by an array of zeros and ones.

1) the complement of B union E

what i got was 1, 1, 0, 1, 1, 0, 0, 1 but it's wrong. i think the "complement of B" thing threw me off. any help would be greatly appreciated! i just started this course so the answer might be really easy but i don't get it XD also, is there a way to write "the complement of..." as a letter with a line over it? thanks =)
how are the 1's and 0's filled in? i suppose you put a 1 if the set has an element of U and 0 if it doesn't?

for instance, to represent the set A = {algebra} we would write 0,1,0,0,0,0,0,0 ??

if that is the case, this is how to proceed. note that "the compliment of A" (in a given universal set U) means "the set of all elements in U that are not in the set A."

now, $(B \cup E)^c$ = {arithmetic, statistics}, that is the set of all elements in U that are not in either B or E

3. Originally Posted by e____o
let U= {arithmetic, algebra, calculus, geometry, trigonometry, analysis, topology, statistics}

B= {analysis, topology, calculus}
E= {algebra, calculus, geometry, trigonometry, analysis}
in each of the following, represent the given set by an array of zeros and ones.

1) the complement of B union E

what i got was 1, 1, 0, 1, 1, 0, 0, 1 but it's wrong. i think the "complement of B" thing threw me off. any help would be greatly appreciated! i just started this course so the answer might be really easy but i don't get it XD also, is there a way to write "the complement of..." as a letter with a line over it? thanks =)
Question: does "the complement of B union E" mean "(complement of B) union E" or "complement of (B union E).
If it is the first, then first find the complement of B: Since B= {analysis, topology, calculus} or {0, 1, 1, 0, 0, 0, 1, 0} its complement is {1, 0, 0, 1, 1, 1, 0, 1} (That's a good reason for using that notation- just swap 1s and 0s.)
E= {algebra, calculus, geometry, trigonometry, analysis} or {0, 1, 1, 1, 1, 1, 0, 0} so "(complement of B) union E" is {1, 1, 1, 1, 1, 1, 0, 1}, the "bitwise and" of the two.

But (B union E) is {0, 1, 1, 1, 1, 1, 1, 0} and its complement is {1, 0, 0, 0, 0, 0, 0, 1}.

4. Originally Posted by HallsofIvy
Question: does "the complement of B union E" mean "(complement of B) union E" or "complement of (B union E).
If it is the first, then first find the complement of B: Since B= {analysis, topology, calculus} or {0, 1, 1, 0, 0, 0, 1, 0} its complement is {1, 0, 0, 1, 1, 1, 0, 1} (That's a good reason for using that notation- just swap 1s and 0s.)
E= {algebra, calculus, geometry, trigonometry, analysis} or {0, 1, 1, 1, 1, 1, 0, 0} so "(complement of B) union E" is {1, 1, 1, 1, 1, 1, 0, 1}, the "bitwise and" of the two.

But (B union E) is {0, 1, 1, 1, 1, 1, 1, 0} and its complement is {1, 0, 0, 0, 0, 0, 0, 1}.
hi HallsofIvy =)
sorry, i should have been more clear- it's the first one, "(complement of B) union E"
now i see it! thanks so much =) if the complement was for the whole problem i could have got it, it's just when it is for one set that i get confused. thanks for your help!