1. Let U the set of students of the university of Cambridge. Let the subsets of U: A: over 20 years, B: women, C: with social stratum of 1, 2 and 3.
Describe in words the next sets:
a)A
0
∩ C b)A ∪ B c)B
0
∪ C
0

d)(A ∩ C)
0

e)A
0
∪ C
0

f)(A ∪ C)
0

g)A
0
∩ C
0

h)A ∩ B ∩ C
i)A − B j)(A − B) ∩ C k)B 4 C l)A 4 B.
Compare the given description in c) and d) and the given in f) and g), can you conclude something?.

A) A ∩ C means in both sets, in this case A and C, and in this question all students both over 20 years and with social stratum of 1, 2 and 3.

B) A ∪ Bmeans in either set or both, both will do, in this case meaning all students in A or B or any in between, and in this question all students over 20 years and/or are women.

C) As is already explained above, B  ∪ C means in this question all students that are women and/or have social stratum of 1, 2, and 3.

D) This is the same as A). Refer to A).

E) A ∪ C is already explained above, and in this question means all students over 20 years and/or have social stratum of 1, 2, and 3.

F) Same as E). Refer to E).

G) Same as A). Refer to A).

H) A ∩ B ∩ C means in students in all three sets simultaneously, and in this question all students that are over 20 years, women, and with social stratum of 1, 2 and 3.

I) A - B, in set theory would mean all students in A but not in B, in other words the difference. In this question, it would mean all students over 20 years that are not women.

J) (A - B) ∩ C would mean, as already explained above, all students over 20 years that are not women and with social stratum of 1, 2 and 3. Usually, it's easier to treat all unions or intersections or whatnot inside brackets as one whole thing, kind of like how you do algebra.

K) B 4 C is nonsensical, there is nothing in set theory like this.

L) Same as K).

The given description between C) and D) would be that they are the same, and comparing F) and G), it seems that the question is trying to make the point that they are almost the same but defined differently.

Step-by-step explanation:

Hope this helped!

they used 313 gallons of paint

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).