<p>Set R has r members and set S has s members. Set T consists of all unique members of set R and set S combined. If q represents the members common to both sets, which of the following represents the number of members in set T?</p>
<p>(A) q - rs
(B) r - s
(C) r + s + q
(D) r + s - q
(E) r + s - 2q</p>
<p>Why is it E?</p>
<p>Well T is the set of numbers in just one of the sets, not both.</p>
<p>So if you have r + s, not only do you have all the numbers, but the numbers that are in both sets are in there TWICE.</p>
<p>So to get the ones in T, you have to subtract the shared ones, and you have to do it twice, since they were double counted (once in R and once in S). So r + s - 2q</p>
<p>Did that make any sense?</p>
<p>n(R) = r
n(S) = s</p>
<p>2q = n(R n S)</p>
<p>n(T) = n(R u S) = n(R) + n(S) - n(R n S) = r + s - 2q</p>
<p>good explanations above, your first instinct was probably to go with D, but if I remember correctly, this was a "hard" problem... so if it took you 5 seconds to pick D, think again.</p>
<p>I actually took longer to pick D lol</p>
<p>wait why 2 q?</p>
<p>r3n I tried to expand my english skills and used a "hyperbole" :-D. </p>
<p>Aspen, theoretically if you have set R with r members and set S with s members and q and common members of BOTH sets (meaning they constitute r and s) you have to subtract q TWICE. </p>
<p>Practically, we can define set R and S. Let r= (1, 2, 3, 4, 5), let s= (3,4,5,6,7,8,9). Thus T = (1,2,6,7,8,9) or 6 elements which is equal to the sum of the number of elements in r and s (12) - 2(common elements aka 3,4,5) = 12 - 2(6) = 6. </p>
<p>If you don't automatically see the first solution, pick some numbers and convince yourself that E is true and not D.</p>
<p>what if you pick a set and it didn't have any unique or common members?</p>
<p>with your picked set, you would therefore be stuck with C, D, and E, r3n (q would be 0). in order to solve it empirically as that, you'd have no choice but to use sets that have common elements.</p>
<p>sub numbers
like r=15 q=5 s=10</p>