Questions: Question 6 5/6 answered A survey of 134 people was conducted at a local community college, and it was found that 46 people carried a cell phone, 64 people carried a tablet computer, and 1 carried both a cell phone and a tablet. (a) How many people carried a cell phone or a tablet? (b) How many people carried neither a cell phone nor a tablet? (c) How many people carried a cell phone only? Submit

Solution Steps

To solve these problems, we can use the principle of inclusion-exclusion and basic set operations.

(a) To find how many people carried a cell phone or a tablet, we use the formula for the union of two sets: |A ∪ B| = |A| + |B| - |A ∩ B|, where |A| is the number of people with a cell phone, |B| is the number with a tablet, and |A ∩ B| is the number with both.

(b) To find how many people carried neither a cell phone nor a tablet, we subtract the number of people who carried either from the total number of people surveyed.

(c) To find how many people carried a cell phone only, we subtract the number of people who carried both from the number of people who carried a cell phone.

To find the number of people who carried either a cell phone or a tablet, we use the principle of inclusion-exclusion. The formula is:

\[ |A \cup B| = |A| + |B| - |A \cap B| \]

where:

• \(|A|\) is the number of people with a cell phone, which is 46.
• \(|B|\) is the number of people with a tablet, which is 64.
• \(|A \cap B|\) is the number of people with both, which is 1.

Substituting the values, we get:

\[ |A \cup B| = 46 + 64 - 1 = 109 \]

To find the number of people who carried neither a cell phone nor a tablet, we subtract the number of people who carried either from the total number of people surveyed:

\[ \text{Neither} = \text{Total} - |A \cup B| = 134 - 109 = 25 \]

To find the number of people who carried only a cell phone, we subtract the number of people who carried both from the number of people who carried a cell phone:

\[ \text{Cell Phone Only} = |A| - |A \cap B| = 46 - 1 = 45 \]

Final Answer