A survey of 182 persons was conducted at TCC, and it was found that 97 persons carried a cell phone, 5 t persons carried a tablet computer, and 8 carried both a cell phone and a tablet. 1. How many people carried a cell phone or a tablet? 2. How many people carried neither a cell phone nor a tablet? 3. How many people carried a cell phone only? 4. How many people carried a tablet but not a cell phone? 1

To solve the problem, we can use the principle of inclusion-exclusion and set notation. Let's define the following: - Let \( A \) be the set of people who carry a cell phone. - Let \( B \) be the set of people who carry a tablet. From the problem, we have the following information: - \( |A| = 97 \) (people carrying a cell phone) - \( |B| = 5 \) (people carrying a tablet) - \( |A \cap B| = 8 \) (people carrying both a cell phone and a tablet) Now, we can answer the questions step by step. ### 1. How many people carried a cell phone or a tablet? Using the principle of inclusion-exclusion, the number of people who carried either a cell phone or a tablet is given by: \[ |A \cup B| = |A| + |B| - |A \cap B| \] Substituting the values: \[ |A \cup B| = 97 + 5 - 8 \] Calculating this gives: \[ |A \cup B| = 94 \] ### 2. How many people carried neither a cell phone nor a tablet? To find the number of people who carried neither, we subtract the number of people who carried either a cell phone or a tablet from the total number of surveyed persons: \[ \text{Neither} = \text{Total} - |A \cup B| = 182 - 94 \] Calculating this gives: \[ \text{Neither} = 88 \] ### 3. How many people carried a cell phone only? The number of people who carried only a cell phone can be found by subtracting those who carried both from those who carried a cell phone: \[ \text{Cell phone only} = |A| - |A \cap B| = 97 - 8 \] Calculating this gives: \[ \text{Cell phone only} = 89 \] ### 4. How many people carried a tablet but not a cell phone? The number of people who carried only a tablet can be found by subtracting those who carried both from those who carried a tablet: \[ \text{Tablet only} = |B| - |A \cap B| = 5 - 8 \] Since \( |B| < |A \cap B| \), this means that there are no people who carried only a tablet. Thus: \[ \text{Tablet only} = 0 \] ### Summary of Results: 1. People who carried a cell phone or a tablet: **94** 2. People who carried neither a cell phone nor a tablet: **88** 3. People who carried a cell phone only: **89** 4. People who carried a tablet but not a cell phone: **0**