1. Statement: We have a total of 140 people. 15 of them like neither TV nor Radio. 80 like Radio. 53 like TV. 2. Define sets and numbers: Let $U=140$ denote the total number of people. Let $|R|=80$ denote the number who like Radio. Let $|T|=53$ denote the number who like TV. Let $|N|=15$ denote the number who like neither. 3. Compute the size of the union: The number who like at least one of TV or Radio is given by $|T\cup R|=U-|N|$. Substitute the numbers: $$|T\cup R|=140-15=125$$ 4. Apply inclusion-exclusion to find the intersection: Use the formula $|T\cap R|=|T|+|R|-|T\cup R|$. Substitute the values: $$|T\cap R|=53+80-125=8$$ 5. Interpretation and final answer: Therefore 8 people like both TV and Radio. Final answer: $|T\cap R|=8$.