A survey of registered voters was conducted to analyze their primary news sources: Television (), the Internet (), and Print newspapers (). The survey revealed the following results:
- voters get news from Television.
- voters get news from the Internet.
- voters get news from Print newspapers.
- voters get news from both Television and Print newspapers.
- voters get news from both the Internet and Print newspapers.
- voters get news from all three sources.
- voters do not get news from any of these three sources.
How many of the surveyed voters get news from Television and the Internet, but NOT from Print newspapers?
Answer: 35 voters
Answer
35 voters get news from Television and the Internet, but not from Print newspapers.
Using the principle of inclusion-exclusion for three sets, the total union size is 230 voters (250 total minus 20 who use none). Setting up the formula 230 = 140 + 150 + 80 - 45 - 60 - |T ∩ I| + 30 allows us to solve for |T ∩ I| = 65. To find those who use Television and Internet but NOT Print newspapers, we subtract the 30 voters who use all three sources from 65, resulting in 35 voters.
Step-by-Step Solution
Key Concept
Three-Set Principle of Inclusion-Exclusion