سوال ۱۱۷ کنکور ارشد علوم کامپیوتر ۱۴۰۱

Apply the inclusion–exclusion principle to find the fraction of students who have at least one kind of internet, then take the complement.

Let $F$ be the set of students with fixed internet and $M$ the set with mobile internet (percentages of the whole student body):

$|F| = 96\%, \qquad |M| = 42\%, \qquad |F \cap M| = 39\%.$

The fraction having at least one type of internet is

$|F \cup M| = |F| + |M| - |F \cap M| = 96 + 42 - 39 = 99\%.$

The students with no internet are the complement of $F \cup M$:

$100\% - |F \cup M| = 100 - 99 = 1\%.$

So $1\%$ of the students have no internet at all, which is option (1).

Exam trick: With two sets, always add the two totals and subtract the overlap once (it was double-counted). Forgetting to subtract $|F \cap M|$ gives $138\%$ — an impossible value, a quick sanity flag.