An analysis of 100 personal injury claims made upon a motor insurance company revealed that loss or injury in respect of an eye, an arm, a leg occurred in 30, 50 and 70 cases, respectively. Claims involving this loss or injury to two of these members numbered 44. How many claims involved loss or injury to all the three, we must assume that one or another of three members was mentioned in each of the 100 claims?

Explanation

To solve the problem, we will use the principle of inclusion-exclusion and set theory. Let's break down the solution step by step.

### Step 1: Define the Sets
Let:
- \( E \) = Set of claims involving eye injuries
- \( A \) = Set of claims involving arm injuries
- \( L \) = Set of claims involving leg injuries

...