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Miscellaneous Exercise 1 · Q151

Q.Write the truth values of the following statement: ∀ n∈N, n+6>8\forall\, n \in N,\ n + 6 > 8.

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The statement claims n+6>8n+6>8 (i.e. n>2n>2) holds for EVERY natural number nn. But n=1n=1 gives 1+6=71+6=7, and 77 is not greater than 88 — a counterexample. (Also n=2n=2 gives 88, not >8>8.) Since the universal claim fails for at least …

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