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Let p denote: “A glass is half empty.” Let q denote: “A glass is half full.” The statement “p if and only if q” is equivalent to which of the following?

1. A glass is half empty and half full
2. A glass is half empty if and only if it is half full
3. Both (a) and (b)
4. None of these

Correct answer: A glass is half empty if and only if it is half full

Solution

With p = 'glass is half empty' and q = 'glass is half full', 'p if and only if q' translates literally to 'A glass is half empty if and only if it is half full.'

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