By inclusion/exclusion,

We have

so that

Now,

and by inclusion/exclusion,

Decompose
into the union of two disjoint sets:

Since they're disjoint,




From the Venn diagram, we see there are 3 elements unique to
- by the way, this is the set
- so
, and it follows that

Finally, we get for (a)

For (b), we have by inclusion/exclusion that

The number of miles that Jose will have left after resting will be 1 1/8 miles.
Total distance to be covered = 2 3/4 miles
Distance traveled = 1 5/8 miles
Therefore, in order to get the distance that's left for Jose to complete his journey, we've to subtract the distance traveled from the total distance and this will be:
= 2 3/4 - 1 5/8
= 2 6/8 - 1 5/8
= 1 1/8
Therefore, he has 1 1/8 miles left to travel.
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Hello!
The last one is no solution because the graphs do not intersect.