The problem statement:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose P(x). And if I want to write "For exactly one x, P(x) then:

If we write ∃x[P(x) ∧ ∀y{P(y) → x = y}]. This is as per answer in the books.

Now, suppose P(y) is false. It will still mean x = y.

Shouldn't it be ∃x[P(x) ∧ ∀y{P(y)↔x = y}]

Same problem with ∃x[P(x) ∧ ∀y{x≠ y→ ¬ P(y)}]

Thanks

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# I Nested Quantifier Problem

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