The table above shows the result of a survey of 100 voters who responded 'Favorable' or 'Unfavorable' or 'Not Sure' about their opinions about two proposals A and B, If the number of voters who did not respond 'Favorable' for either proposal was 40, what was the number of voters who responded 'Favorable' for both proposals?

Explanation: Total voters = 100. Number who did not respond 'Favorable' for either A or B (\((A \cup B)^c\)) = 40. Number who responded 'Favorable' for A or B or both (\(A \cup B\)) = \(100 - 40 = 60\). Number who responded 'Favorable' for A (\(A\)) = 40 (from table). Number who responded 'Favorable' for B (\(B\)) = 30 (from table). We need the number who responded 'Favorable' for both (\(A \cap B\)). Using the Principle of Inclusion-Exclusion: \(|A \cup B| = |A| + |B| - |A \cap B|\). \(60 = 40 + 30 - |A \cap B|\). \(60 = 70 - |A \cap B|\). \(|A \cap B| = 70 - 60 = 10\).