Here is how I have solved,
The statements provided by Mrs. Baker can be represented as follows and these are “True statements”
- ~ Bill is youngest → Alice is youngest
- ~ Carl is youngest → ~ Alice is youngest
Now lets consider each option
Option A : Alice is youngest. If we consider this true then
LHS of statement 1 is true hence RHS must be true for statement 1 to be true so Alice is youngest is true. This favors our assumption
Now if we see 2nd statement the LHS is true hence RHS must also be true for statement 2 to be true which means Alice is not youngest is true. This doesn't favors our assumption
Hence option A cannot be true
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Option B : Bill is youngest. If we consider this true then
LHS of statement 1 is false hence RHS can be anything for statement 1 to be true but in this case RHS will be false (because only one of them is youngest and we have assumed Bill is youngest) so Alice is youngest is false i.e. Alice is not youngest
Now if we see 2nd statement the LHS is true hence RHS must also be true for statement 2 to be true which means Alice is not youngest
Hence there is no contradiction the conclusions of both the statements is same so B is a possible answer.
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Option C : Carl is youngest. If we consider this true then
LHS of statement 1 is true hence RHS must also be true for statement 1 to be true so Alice is youngest is true. This contradicts our assumption hence Carl cannot be youngest so option C cannot be answer.
Hence B is the only possible answer. @GO Classes please let me now if this argument is correct or not?