Question 1076130: PLEASE HELP ASAP!!
Let A= {2,5,8,z,$}, B={5,^,z,8,p}, and C={2,z,9,p,△} Find the following:
a) A U (B ∩ C)
b) (A U B) ∩ C
c) A ∩ (B U C)
d) A ∩ (B U C)
e) Find n(A x B)
Thank you in advance
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! A= {2,5,8,z,$}, B={5,^,z,8,p}, and C={2,z,9,p,△}
The best way is to substitute the sets for the letters.
Make the parentheses big as necessary. I'll just do (c)
A ∩ (B U C)
æ ö
{2,5,8,z,$} ∩ ç{5,^,z,8,p} U {2,z,9,p,△}÷
è ø
We do inside the parentheses first and bring the other
part down to the next line:
U between two sets means to put all the elements that
are in one or both sets all into one set. [Don't repeat
the element if it is in both sets, just list it one
time only) Bring everything else down to the next line:
{2,5,8,z,$} ∩ {5,^,z,8,p,2,9,△}
∩ between two sets means to put ONLY those elements which
are IN COMMON to both sets into one set.
{2,5,8,z}
You do the rest. If you have trouble, you can tell me in
the thank-you note form below, and I'll get back to you
by email.
Edwin
Answer by AnlytcPhil(1807)  (Show Source):
You can put this solution on YOUR website!
OK, I'll also do e). I'm the same "Edwin" as the "Edwin" above. :)
n(A×B)
When there is an × between two sets, that means to make all
possible ordered pairs of elements, where each ordered pair
of elements has its first coordinate from the first set and
the second coordinate from the second set. So
A×B = { (2,5),(2,^),(2,z),(2,8),(2,p),
(5,5),(5,^),(5,z),(5,8),(5,p),
(8,5),(8,^),(8,z),(8,8),(8,p),
(z,5),(z,^),(z,z),(z,8),(z,p),
($,5),($,^),($,z),($,8),($,p) }
n(A×B) means the number of elements in A×B.
That, of course is 25, which can be gotten by multiplying
the number of elements in A, which is n(A), by the number
of elements in B, which is n(B).
So n(A×B) = n(A)∙n(B) = 5∙5 = 25.
It is not necessary to write out all the elements of A×B
as I did above, when you're only asked for n(A×B). If
that's all you're asked to find, you only need to multiply
the numbers of elements in them. I only wrote all of A×B
out to show you what A×B means. [BTW, don't use the same
symbol for set multiplication as you use for number
multiplication. I used × for set multiplication and ∙
for number multiplication].
Edwin
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