证明：[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶数量矩阵[tex=9.929x4.071]s4iFwJNC/D8533R68c8pxvpWZ4vJALEA3Q5rJcgChDQ6lhDTOQSPQWHpiUlAopGXAQlyAl9V93UDm6G4rN1mOD4YZUzzYqjXPegpiJIVKFTDg0LEpcduEceOqjNyj66YrRkn41rEwNJ3r0a5nVLqKw==[/tex]与任意[tex=0.643x1.286]ZsZs11iKEvfmzDIurZth8g==[/tex]阶矩阵[tex=0.786x1.286]q1djlrfSWHAqH21hBgtrSw==[/tex]可交换，即[tex=4.357x1.286]ZHtkzddb6nCZKhzGq6vKqw==[/tex]．

设矩阵[tex=10.071x3.5]QN0fTQbn6M33pU3gx/S2shauyFS3+ACuvjCeR4/plRK+Ar/k8T5+D2k4F69nSXVH7uae8ESD+UaiI7VoVixG0VymXeWft/sOsGxPdl5v/pbKPjBAtNElsnvPQ7GCxvMejMPGNgxUq5qm9lC+NbypQIdG002sZGhmg8RjTECJd4Nkex1fdMAXGfHBHtZmaU/8[/tex],[tex=9.929x4.071]opqi7S5YyIUs5JQiNQr2vNAXVg3BXAPxe7wSDgfNpByPjU8aoa+gUU9+XxBepbwpY5YfaK+O+K7Az7Isl8btr7auYxcZu2Bzrsm3oUfVg4R4dA8n5bqKcyiT98HgWFGZDAxY7AlD0blNlIptqk3n8LSdbwhkQ8XR1ejaU8NF3e0atZDHaDpieF3QihxUwe4X[/tex],[tex=9.786x3.5]2dkVCjufgjJKA1Jpl3dseuOZzowpS59HPk22eBA0xFhE3jVpCdEiJMxkuq/nF8I8rsspwhAqETkLr1p43WewcHej83ez13fmKNnwkQdpCeav/aTL/ObkfGVpxYvxr8WjhRMGEW7jTh3QgyICQVHWaPXHli1mn9ZvlJFc0qkwMrqAbD2Lc8gRH9Dxy+sJsRRu[/tex],若矩阵$[tex=6.786x2.786]cUyiQVfXVPAX7qbpaubKY/kSim9pWfxGB/6NSsnRGj8ldNZiffB5gl73zp3KMiI3qe8xcwvZ8Gq4Bn2EpdK6UQ==[/tex],证明:[tex=5.071x1.357]E3Rcs/uaZmoNBP9KoeiSGieV2Auo9jOBRkM8qsuc/dk=[/tex].

下列变量组（）是一个闭回路。 A: {x，x，x，x，x，x} B: {x，x，x，x，x} C: {x，x，x，x，x，x} D: {x，x，x，x，x，x}

以下谓词蕴含式正确的是（）: (∀x) (A(x)→B(x))=>( ∀x)A(x)→(∀x)B(x)|(∀x) (A(x)↔B(x))=>( ∀x)A(x)↔(∀x)B(x)|(∀x)A(x)∨(∀x)B(x)=>( ∀x) (A(x)∨B(x))|(∃x) (A(x)∧B(x))=>(∃x)A(x)∧(∃x)B(x)

以下谓词蕴含式正确的是（）: (?x) (A(x)→B(x))=>( ?x)A(x)→(?x)B(x)|(?x) (A(x)?B(x))=>( ?x)A(x)?(?x)B(x)|(?x)A(x)∨(?x)B(x)=>( ?x) (A(x)∨B(x))|(?x) (A(x)∧B(x))=>(?x)A(x)∧(?x)B(x)

下列式中错误的是： A: (∀x)(A(x)Úp(x)) Û (∀x)A(x)Ú (∀x)p(x) B: ($x)A(x) Ù p Û ($x)(A(x) Ù p ) C: (∀x)(A(x)ÚB(x)) Þ (∀x)A(x)Ú( ∀x)B(x) D: ($x)(A(x)ÙB(x)) Þ ($x)A(x)Ù( $x)B(x)

判断下列推证是否正确。 (∀x)(A(x)→B(x))⇔(∀x)(￢A(x)∨B(x)) ⇔(∀x)￢( A(x)∧￢B(x) ) ⇔￢(∃x) ( A(x)∧￢B(x) ) ⇔￢( (∃x)A(x)∧(∃x)￢B(x) ) ⇔￢(∃x)A(x)∨￢(∃x)￢B(x) ⇔￢(∃x)A(x)∨(∀x)B(x) ⇔(∃x)A(x)→(∀x)B(x)

以下谓词公式中，( )不是逻辑有效式。 A: ($x)(P(x)∧Q(x)) Þ ($x) P(x)∧($x) Q(x) B: ("x)(P(x)∧Q(x)) Þ ("x) P(x)∧("x) Q(x) C: ($x)(P(x)∧Q(x)) Û ($x) P(x)∧($x) Q(x) D: ("x)(P(x)∧Q(x)) Û ("x) P(x)∧("x) Q(x)

以下谓词公式中，( )不是逻辑有效式。 A: ($x) P(x)∨($x) Q(x) Þ ($x)(P(x)∨Q(x)) B: ("x) P(x)∨("x) Q(x) Þ ("x)(P(x)∨Q(x)) C: ($x) P(x)∨($x) Q(x) Û ($x)(P(x)∨Q(x)) D: ("x) P(x)∨("x) Q(x) Û ("x)(P(x)∨Q(x))

使用下述谓词：P(x): x是语言、Q(x): x是中间语言、R(x): x是世界通用的，及量词表示自然语句“没有语言是世界通用的话，就至少有一种中间语言存在”为（ ）。A.~($x)(P(x) Þ R(x)) Þ ($x) Q(x)B.~($x)(P(x)∧R(x)) ∧ ($x) Q(x) C.~($x)(P(x) Þ R(x)) ∧ ($x) Q(x) D.~($x)(P(x)∧R(x)) Þ ($x) Q(x) A: ~($x)(P(x) Þ R(x)) Þ ($x) Q(x) B: ~($x)(P(x)∧R(x)) ∧ ($x) Q(x) ~($x)(P(x) Þ R(x)) ∧ ($x) Q(x) D.~($x)(P(x)∧R(x)) Þ ($x) Q(x) C: ~($x)(P(x) Þ R(x)) ∧ ($x) Q(x) D: ~($x)(P(x)∧R(x)) Þ ($x) Q(x)