Re: Of the 60 trucks sold by a dealer in a month, 40 have air-bag
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20 May 2025, 04:00
A dealer sold 60 trucks in a month with the following features:
- 40 trucks have air-bags.
- 25 trucks have power-steering.
- 7 trucks have both air-bags and power-steering.
We need to find how many trucks have neither air-bags nor power-steering.
Step 1: Understand the Given Data
- Total trucks sold: 60
- Trucks with air-bags (A): 40
- Trucks with power-steering (P): 25
- Trucks with both $\((\mathrm{A} \cap \mathrm{P}): 7\)$
Step 2: Use the Principle of Inclusion-Exclusion
To find the number of trucks with at least one feature (air-bags or power-steering or both), use:
Trucks with A or $\(\mathrm{P}=\mathrm{A}+\mathrm{P}-\mathrm{A} \cap \mathrm{P}\)$
$$
\(=40+25-7=58\)
$$
Step 3: Calculate Trucks with Neither Feature
Subtract the trucks with at least one feature from the total:
$$
\(\begin{aligned}
\text { Trucks with neither } & =\text { Total }- \text { Trucks with } \mathrm{A} \text { or } \mathrm{P} \\
= & 60-58=2
\end{aligned}\)
$$