作者priest0204 (香香)
看板logic
標題[請益] 數理邏輯 The Predicate Calculus. Validity
時間Sun Jan 17 14:57:12 2010
Let x and y be variables, A(x),B(x), and A(x,y) be any formulas,
and A be any formula not containing any free occurrences of x.
Then
1.╞(exist x)(A(x)orB(x))←→(exist x)A(x)or(exist x)B(x)
2.╞(for all x)A(x)or(for all x)B(x)→(for all x)(A(x)orB(x))
3.╞(exist x)(AorB(x))←→Aor(exist x)B(x)
Discuss the validity of formulas 1,2 and 3
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Vertify the equivalence of the left- and right-hand members of each of the
following pairs of formulas.
1. (exist x)(y)~(y＞x),(exist x)~(exist y)(y＞x)
2. (exist x)(y)(y＞xor~(y＞0)),(exist x)(y)(y＞0→y＞x)
3. (x)(exist y)(exist z)(x＜yandz^2＞y),(x)(exist y)(x＜yand(exist z)(z^2＞y))
註: 有些符號我不會所以打 (for all)(倒A) (exist)(倒E) and or 造成閱讀不便 請見諒
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1F：推 earh:~是什麼意思，後面三題有點看不懂 01/17 21:40
2F：推 Rishia:negation 01/17 21:57
3F：→ yauhh:第二段的(y)或 (x)是表達(for all y), (for all x)嗎? 01/18 01:17
4F：→ priest0204:對 是 for all 01/19 21:06