A couple of problems on set theoretic manipulations and / or percentages Problem 1:
A public opinion poll shows that 93% of the people agree with the government on the first decision, 84% on the second, and 77% on the third, for the three decisions made by the government. At least what percentage of the population in question agreed with the government on all three decisions? 
Problem 2: 
If 70% of all the disabled war veterans of a country have lost an eye, 75% an ear, 80% an arm, and 85% a leg, then at least what percentage must have lost all four? 
 A: Hint:  to have the fewest number that share all three or four characteristics, you want all the rest to be missing only one.  So for the first problem, assume all the ones that disagree on the first agree on the next two and so on.  What is the total number of disagreers?
A: Problem 1: 
First we try to estimate the percentage of people who have disagreed on at least one of the decisions: there are $7\%$ people who've disagreed on the first decision, $16\%$ on the second, and $26\%$ on the third. So, if no two of these three groups of disagreers have any members in common, then $7+16+26$ $=$ $49\%$ of the people have disagreed on at least one of the three decisions. However, the above three groups of disagreers may have members in common; so at most $49\%$ of the people have disagreed on at least one of the three decisions. Hence at least $51\%$ have agreed on all three decisions. 
Problem 2: 
Amongst the disabled veterans who have not lost all four of the limbs, we note that $30\%$ have not lost an eye, $25\%$ have not lost an ear, $20\%$ have not lost an arm, and $15\%$ have not lost a leg. So at most $30+25+20+15$ $=$ $90\%$ of the disabled veterans have not lost all four of the limbs. Hence at least $10\%$ have lost all four. 
Is my reasoning correct? And if so, have I managed to arrive at the correct answer too? 
