(<em>A</em> ∩ <em>B</em>)' is the complement of <em>A</em> ∩ <em>B</em>, or the set of all elements in the universal set <em>U</em> that do not belong to <em>A</em> ∩ <em>B</em>.
<em>A</em> ∩ <em>B</em> is the intersection of <em>A</em> and <em>B</em>, or the set of all elements common to both <em>A</em> and <em>B</em>.
We have
<em>A</em> = {q, s, u, w, y}
<em>B</em> = {q, s, y, z}
so that
<em>A</em> ∩ <em>B</em> = {q, s, y}
Then
(<em>A</em> ∩ <em>B</em>)' = {r, t, u, v, w, x, z}
which makes (c) the answer.
<h2>
Answer:</h2><h2>
Samuel fell asleep after travelling 90 miles which is 15%of their total trip distance.</h2>
Step-by-step explanation:
The total length of the trip = 600 miles
Samuel fell asleep after they had travelled = 90 miles
Percentage of the total trip travelled when samuel fell asleep = 
= 15%
Samuel fell asleep after travelling 90 miles which is 15%of their total trip distance.
Probability that both roads from a to b are blocked is the product of the individual probabilities, i.e.
P(~ab)=0.25*0.25=0.0625
Similarly
P(~bc)=0.25*0.25=0.0625
Probability that EITHER one or both of ab and bc are blocked is the sum of the probabilities:
P(~ab ∪ ~bc)=0.0625+0.0625=0.125
(recall that one cannot travel from a to c if either ab or bc is blocked.)
Therefore the probability that there exists an open route from a to c
= P(ac) = 1-P(~ab ∪ ~bc)
= 1 - 0.125
=0.875
1-0.15=0.85
36.21/0.85=42.6=ANSWER
