In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how ma

Step 1: Write the set theory formula
n(English ∪ French) = n(English) + n(French) – n(Both)
Where ∪ means union (all people)

Step 2: Identify known values
Total people = 500
English speakers = 350
French speakers = 400
Both = ?

Step 3: Substitute into formula
500 = 350 + 400 – Both
500 = 750 – Both

Step 4: Solve for Both
Both = 750 – 500
Both = 250

Step 5: Verify the logic
If we add 350 + 400 = 750 language skills
But only 500 people exist
The extra 250 skills must be from people counted twice (speaking both languages)