SOLUTION: One and only one of five statements referring to our esteemed President is true. Assume that he either likes or dislikes any vegetable. Because of logical consistency, you should b

Question 262010: One and only one of five statements referring to our esteemed President is true. Assume that he either likes or dislikes any vegetable. Because of logical consistency, you should be able to infer which is the true statement.
The statement are:
a) President Obama likes broccoli, spinach, and beets.
b) As regards beets and asparagus, President Obama likes one and dislikes the other.
c) President Obama likes beets.
d) President Obama likes asparagus
e) President Obama likes both broccoli and spinach.
Which is the true statement? Which of these vegetables does our Chief Executive dislikes? (Use deductive reasoning to decide.)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If a) is true, then certainly e) is true. But we only want one true statement. So a) cannot be true.

If b) is true, then either c) or d) is true. Either way, we have 2 possible scenarios with 2 true statements, but we only want one true statement. So b) cannot be true.

Here's where things get a bit tricky, but try to follow as close as you can. If c) is true, and d) is false (since we only want one true statement), then this automatically makes b) true. On the flip side, if d) is true, and c) is false, then b) is again automatically true. In either case, if c) or d) are true, then b) is true. But we only want one true statement. So c) and d) cannot be true.

By process of elimination, every statement was shown to be false. So the only remaining statement e) must be true in order to satisfy the problem's requirements.
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