Worked Example 1
In a group of 50, 30 read the newspaper, 22 listen to the radio, and 12 do both. Find how many do neither.
Step 1: the middle12 into the overlap.
Step 2: the crescentsNewspaper only 18, radio only 10.
Step 3: the corner10 do neither.
Step 4: check18 + 12 + 10 + 10 = 50, which is n(U).
Worked Example 2
In a class of 35, 20 play chess, 5 play neither, and 4 play both. How many play carrom?
Fill in what you knowMiddle 4, corner 5, chess only 16. One region is still unknown.
Use the total16 + 4 + (carrom only) + 5 = 35, so carrom only = 10.
Answer the question asked14 play carrom altogether, since the 4 who play both are carrom players too.
The trap in this questionA circle total includes the overlap; a crescent does not. Reread what was asked.
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