湖北大学2004-2005学年度第二学期课程考试试题纸(第1页共4页) 长黃兴 湖北课程考试试题纸 兴兴兴 课程名称: 数理逻辑 考试方式: (闭卷) 印刷份数:_28 学院 哲学系任课教师:_宋伟 专业年级 哲学2003级 兴兴兴兴兴兴兴 三|三|四五六七|八阅卷 教师 ,,,,,, Complete the following blanks. (each 2 points, total 20 points) 製 分 *1. For a statement form involving n different statement variables, there are__distinct truth functions with n places 2. If A and b are statement forms, a is to b if(a<>B)is a tautology *3. For the connectives V,∧,→and>, the pairs{~,∧}, *adequate sets of connectives *4. The Adequacy Theorem for the formal system L: 5. Translate the statement "Every number is either odd or even. into symbols *6. A formal language consists of a set of and a set of 7. The formal system L is i. e there is an effective method for deciding, given ****any wfof L, whether it is a theorem ofL. 8. In the wf(V Xi)A, we say that A is the of the quantifier 兴兴 暑兴兴兴|9. Any infinite subset of a countable( or denumerable)is ***10.(V x)(3x2)(V X3)A1 (x1, X2,x3)yields a Skolemised form 说明:本试卷将作为样卷直接制版胶印,请命题教师在试题之间留足答题空间
湖北大学 2004—2005 学年度第二学期课程考试 试题纸（第 1 页 共 4 页） 说明： 本试卷将作为样卷直接制版胶印，请命题教师在试题之间留足答题空间。 课程考试试题纸 课程名称： 数理逻辑 （ A 卷） 考试方式： （闭卷） 印刷份数： 28 学 院： 哲 学 系 任课教师： 宋 伟 专业年级： 哲学 2003 级 题 号 一 二 三 四 五 六 七 八 总分 阅卷 教师 得 分 …………………………………………………………………………………………………… 一. Complete the following blanks. (each 2 points, total 20 points) 1. For a statement form involving n different statement variables, there are distinct truth functions with n places. 2. If A and B are statement forms, A is to B if (A B) is a tautology. 3. For the connectives ～,∨,∧,→ and , the pairs {～,∧}, , and are adequate sets of connectives. 4. The Adequacy Theorem for the formal system L: . 5. Translate the statement ‘Every number is either odd or even.’ into symbols: . 6. A formal language consists of a set of and a set of . 7. The formal system L is , i.e. there is an effective method for deciding, given any wf. of L, whether it is a theorem of L. 8. In the wf. ( xi) A, we say that A is the of the quantifier. 9. Any infinite subset of a countable (or denumerable) is . 10. ( x1) ( x2) ( x3) 3 A1 (x1,x2,x3) yields a Skolemised form: . 得 分 * * * * * * * * * * * 学 号： 姓 名： * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 学 院： 专业年级： * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
湖北大学2004-2005学年度第二学期课程考试试题纸(第2页共4页) =. Solve the following problems. (each 10 points, total 50 points) Find the disjunctive normal form and the conjunctive normal form which are logically equivalent to(p<>q) 2. Find a statement form involving only i which is logically equivalent to(p-q) 3. Determine whether the argument form(p(vr)),(r);.((9)(p) is valid or 说明:本试卷将作为样卷直接制版胶印,请命题教师在试题之间留足答题空间
湖北大学 2004—2005 学年度第二学期课程考试 试题纸（第 2 页 共 4 页） 说明： 本试卷将作为样卷直接制版胶印，请命题教师在试题之间留足答题空间。 二. Solve the following problems. (each 10 points, total 50 points) 1. Find the disjunctive normal form and the conjunctive normal form which are logically equivalent to (p q). 2. Find a statement form involving only ↓ which is logically equivalent to (p→q). 3. Determine whether the argument form (p→ (q∨r))，(～r); ∴ ((～q)→(～p)) is valid or invalid. 得 分
湖北大学2004-2005学年度第二学期课程考试试题纸(第3页共4页) 4. Using the Deduction Theorem for L, Show that the following wf. is theorem of L, Where a and B are any fs. ofL (A→B)→(~(B→C)→~A)→(A→C)) 5. Find an interpretation in which the wf.(V XI(A+(X1, X2)A,(X2, X1) is interpreted by a statement which is false =.Proof. (each 10 points, total 30 points) 分 Prove that if the argument form Al, A2, "". An: . A is valid then the statement form, (AIM ∧An)→A) is a tautology 说明:本试卷将作为样卷直接制版胶印,请命题教师在试题之间留足答题空间
湖北大学 2004—2005 学年度第二学期课程考试 试题纸（第 3 页 共 4 页） 说明： 本试卷将作为样卷直接制版胶印，请命题教师在试题之间留足答题空间。 4. Using the Deduction Theorem for L, Show that the following wf. is theorem of L, Where A and B are any wfs. of L. ((A→B)→((～(B→C)→ ～A)→ (A→C))) 5. Find an interpretation in which the wf. ( x1)( 2 A1 (x1,x2)→ 2 A1 (x2,x1)) is interpreted by a statement which is false. 三. Proof. (each 10 points, total 30 points) 1. Prove that if the argument form A1,A2,…,An；∴A is valid then the statement form, (A1∧… ∧An)→A) is a tautology. 得 分
湖北大学2004-2005学年度第二学期课程考试试题纸(第4页共4页) 2. Prove that the formal system L is consistent 3. Prove that if, in a particular interpretation I, the wfs. A and(A-B)are true, then B is also 说明:本试卷将作为样卷直接制版胶印,请命题教师在试题之间留足答题空间
湖北大学 2004—2005 学年度第二学期课程考试 试题纸（第 4 页 共 4 页） 说明： 本试卷将作为样卷直接制版胶印，请命题教师在试题之间留足答题空间。 2. Prove that the formal system L is consistent. 3. Prove that if, in a particular interpretation I, the wfs. A and (A→B) are true, then B is also true