※ 引述《mqazz1 (無法顯示)》之銘言： : A set {bi} of two-valued boolean functions is said to be complete if every two-valued boolean function can be expressed by a boolean expression using only bi's : Define boolean functions → and ⊥ as follows: : a→b ≡ ~aˇb : a⊥b ≡ F : which of the following set is not complete? : (A) { ~, ˇ} : (B) {⊥, →} : (C) { ~, →} : (D) { ^, →} : 87交大資科27題 : http://ppt.cc/7RIR 能用來表示 (~,and, or) 的即為 complete (A) a^b = ~(~av~b) avb = trivial ~a = trivial (B) ~a = a->a⊥b ( if a = 1, ~a = 1->1⊥b = 1-> F = F = 0 if a = 0, ~a = 0->0⊥b = 0->F = T = 1 ) avb = ~a->b ( ~a 再用上式帶入 ) a^b = ~(~av~b) (因為 ~ 和 v 可用 ⊥ 及 -> 代替, 故 ^ 也可 ) (C) ~a = trivial a^b = ~(~av~b) = ~(a->~b) avb = ~a->b 所以 D 不是 答案對嗎? --

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