This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back selorm — been a while! Let's pick up where you left off. Here's the solution for problem 1: Let M be the set of students who study Mathematics, S for Science, and E for English. Given: Total students = 40 |M| = 22 |S| = 18 |E| = 15 |M S| = 8 |M E| = 5 |S E| = 4 |M S E| = 2 1. How many study at least one subject? This is equivalent to finding |M S E|. We use the Principle of Inclusion-Exclusion. Step 1: Apply the Principle of Inclusion-Exclusion formula. |M S E| = |M| + |S| + |E| - (|M S| + |M E| + |S E|) + |M S E| Step 2: Substitute the given values into the formula. |M S E| = 22 + 18 + 15 - (8 + 5 + 4) + 2 Step 3: Perform the calculations. |M S E| = 55 - (17) + 2 |M S E| = 38 + 2 |M S E| = 40 The number of students who study at least one subject is 40. 2. How many study none? This is the total number of students minus those who study at least one subject. Step 1: Subtract the number of students studying at least one subject from the total number of students. Number who study none = Total students - |M S E| Step 2: Substitute the values and calculate. Number who study none = 40 - 40 Number who study none = 0 The number of students who study none is 0. Send me the next one 📸