let a and b be sets in some universe u. pick true or false. a) (a – b) is a subset of a
b) (a – b) is a subset of b
c) the complement of the complement of a is equal to a
d) a union (b-a) = a union b

 (a), (c) and (d) are TRUE  and  (b) is FALSE.

Step-by-step explanation:  Given that A and B are sets in some universal set U.

We are to select the true and false statements from the following :

a) (A – B) is a subset of A.

b) (A – B) is a subset of B.

c) The complement of the complement of A is equal to A.

d) A ∪ (B-A) = A ∪ B.

(a) We know that (A - B) contains all those elements of U which are present  in A but not present In B.

So, it will be a subset of set A, not B. The given statement is TRUE.

(b) (A - B)  will be a subset of A, not B. The given statement is FALSE.

(c) Since A complement contains those elements of U which are not present in A, so the complement of A complement contains all those elements of U which are not present in A complement.

Therefore, the complement of A complement contains all elements of U which are present in A.

So, the given statement is TRUE.

(d) We know that

(B - A) contains all elements that are present in B, but not A. So, the union of A and (B - A) contains all elements that are present in A and B both.

That is, A ∪ (B-A) = A ∪ B.

The given statement is TRUE.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

the answer is 489

step-by-step explanation: