A survey of 200 students found that 75 offered MTH 101, 86 offered PHY 101, and 100 offered CS 101. If 28 offered MTH 101 and PHY 101, 22 offered MTH 101 and CS 101, and 26 offered PHY 101 and CS 101,

Here's a step-by-step solution to the problem.

Let $N$ be the total number of students.
Let $M$ be the set of students who offered MTH 101.
Let $P$ be the set of students who offered PHY 101.
Let $C$ be the set of students who offered CS 101.

Given information:
$N = 200$
$|M| = 75$
$|P| = 86$
$|C| = 100$
$|M \cap P| = 28$
$|M \cap C| = 22$
$|P \cap C| = 26