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Exercise B

Avg difficulty 3.0

Explain why:

  1. ‘∃x∀y(A(y)↔x=y)\exists x\forall y(A(y)\leftrightarrow x=y)’ is a good symbolization of ‘there is exactly one apple’.

  2. ‘∃x∃y[¬x=y∧∀z(A(z)↔(x=z∨y=z)]\exists x\exists y\bigl[\neg x=y\wedge\forall z(A(z)\leftrightarrow(x=z\vee y=z)\bigr]’ is a good symbolization of ‘there are exactly two apples’.

Magnus et al., forall x: Calgary, First-order logic, Identity, Exercise B

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Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.