# Some logic practice.
一.
(unit 11) Construct a suitable language for first-order logic (predicate logic), with alphabets and formation rules.
(105, 106, 107)
[[basic-logic/logic-problem-1|logic-problem-1]]
二.
(unit 10) Analyze statements as syllogisms, and prove whether the argument is valid or invalid by (1) Aristotelian method and (2) Venn diagram method. If it is an invalid argument, give a persuasive counterexample.
(105, 106, 107)
[[basic-logic/logic-problem-2|logic-problem-2]]
三.
(unit 12) Translate ordinary language into first-order language expressions.
(105, 106, 107)
[[basic-logic/logic-problem-3|logic-problem-3]]
四.
(unit 13) Use tableaux system to prove whether an argument is valid or not, and specify a counterexample if invalid.
(105, 106, 107)
[[basic-logic/logic-problem-4|logic-problem-4]]
五.
(unit 15) Exemplify logical fallacies and explain the reasoning of why it is a fallacy.
(105, 106, 107)
[[basic-logic/logic-problem-5|logic-problem-5]]
六.
(unit 9, unit 14) Complete the given proofs.
(105, 106, 107)
[[basic-logic/logic-problem-6|logic-problem-6]]
七.
(unit 10) Explain the significance of "existential import" and show how the definition of validity is affected by this concept.
(105)
[[basic-logic/logic-problem-7-e|logic-problem-7-e]]
(unit 12) Briefly explain the content and significance of Russell's theory of description.
(107)
[[basic-logic/logic-problem-7-r|logic-problem-7-r]]
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(∀x)(Sx → Mx), (∃x)(Mx ∧ Px) ⊢ (∃x)(Sx ∧ Px)