Consider a ﬁnite set A = {a1,...,an}, and let P(x) be some statement. – Explain why...

Consider a ﬁnite set A = {a1,...,an}, and let P(x) be some statement.

– Explain why ∀x(x∈A → P(x)) is equivalent to P(a1)∧P(a2)∧...∧P(an).

– Explain why ∃x(x∈A∧P(x)) is equivalent to P(a1)∨P(a2)∨...∨P(an).

(It may help to think about some special cases like n = 2, n = 3. A formal proof is not required here.)

Expert Solution

Colby Messinger answered 2 years ago

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Question

Consider a ﬁnite set A = {a1,...,an}, and let P(x) be some statement. – Explain why...

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