Question 202480: Given U = {All letters of the alphabet}, A = {c, d, e, f}, and B = {e, f, g, h, k}. List the elements of set
(a) A U B
(b) A ∩ B
(c) A′ ∩ B′
(d) A′ U B′
(e) A U B′
(f) (A U B′) ∩ B
(g) (A U B) ∩ (A U B′)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first three to get you started.
Remember, the big "U" (set union) between the two sets tells us to combine the two sets to form a new (possibly larger) set. For example, let's say we have
the two sets
X = {1, 2, 5} and Y = {1, 3, 4, 5}
The union of these two sets is simply the combination of the two sets (remember to remove duplicates)
X U Y = {1, 2, 3, 4, 5}
The upside down U is the set intersection. This just forms a new set with any elements that the two sets have in common. So using the same sets, we get
Take note how 1 and 5 are in both sets
Also, the tick mark right after the set tells you to form a new set with every element in U that is NOT in A. In other words, form the set that has every
letter but the ones found in the given set
So in this case,
and
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a)
Simply combine the two sets (and remove duplicates) to get:
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b)
Since sets A and B only have the elements "e" and "f" in common, this means that:
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c)
Now since the two sets A' and B' (see above) have the elements a, b, i, j, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z in common, this means that
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