Computer Science I / Propositional Logic
Practice question · True or false

The convention that p → q is true whenever p is false exists so that a universal statement is not falsified by cases it never applies to.

Hints
  1. Consider 'every number over 100 in this list is even' with no such number.
  2. A vacuous case should not count as a counterexample.
Show the answer

True

Why

True. 'All swans in this empty lake are green' has to come out true, or a universally quantified claim would be refuted by irrelevant cases. The convention makes ∀x(P(x)→Q(x))\forall x (P(x) \to Q(x)) behave: only an x with P true and Q false counts against it.

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