The inclusion/exclusion principle states that
That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).
Therefore,
will have the most elements when the sets
and
are disjoint, i.e.
, which would mean the most we can can in this case would be
(Note that
denotes the cardinality of the set
.)
This answer seems really hard but just don't overthink it. You pretty much don't have to do any math. It took me forever to do this because I was thinking so hard but i re-read it and the answer was right infront of me.
1.00p + 3.26n = $248.52
He reads 1/11 book in 2/5 hour.
A whole book is 11/11 of a book.
Multiply by 11.
He reads 11/11 book in 11 * 2/5 hour.
He reads 1 book in 22/5 hour.
22/5 hour = 4.4 hour = 4 hours and 24 minutes
Answer:
x ∈ (-∞, 3) U (6, ∞).
Step-by-step explanation:
We use factorization and optain
Then, we have two critical points: x=3 and x=6. Now:
(i) for x < 3 we have that x-6 <0 and x-3 <0. Then (x-6)(x-3) > 0.
(ii) for 3 < x < 6 we have that x -6 <0 and x -3 > 0. Then (x-6)(x-3) < 0.
(iii) for x > 6 we have that x-6 >0 and x-3 > 0. Then, (x-6)(x-3) > 0.
conditions (i) and (iii) satisfy the inequatliy, then the solution is x ∈ (-∞, 3) U (6, ∞).
The graph is in the picture below.
