[請益] 數理邏輯 The Predicate Calculus. Validity

[priest0204 (香香)]

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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推 earh:~是什麼意思，後面三題有點看不懂
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→ yauhh:第二段的(y)或 (x)是表達(for all y), (for all x)嗎?
→ priest0204:對 是 for all