Find the number of elements in a 1 ∪ a 2 ∪ a 3 if there are 200 elements in a 1 , 1000 in a 2 , and 5, 000 in a 3 if (a) a 1 ⊆ a 2 and a 2 ⊆ a 3 . (b) the sets are pairwise disjoint. (c) there are two elements in common to each pair of sets and one element in all three sets.

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let the number of elements in A.

Remember, the number of elements in satisfies

Then,

a) If , and if

Since

So

b) Since the sets are pairwise disjoint

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

d

step-by-step explanation:

d

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1