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)

计算下面的n 级行列式：[tex=12.214x5.786]WXZcTaGnkR24iTdIVn1vhqAv+a9d6Ky9/ET7Mqaji1WXmVkl3uHIP2/SQ42rkjB9/qdyOYFNrYTmUeCZzj5x5KAHYC5F9ElUyQ2oDnLpQyRw35TCiJmBwh63P42v4QhwKDdXkAOdwBjTsi6CE6vfKFe6IJ7U3pawHYXZt8hZCEOfCx63NU2ys3bSOktE/5enZvfxNUaIhX0vBVp/Kp5p9pOL6HDyroPfL7sYckJJYJggFdvlvxKRpjJzOSQk5Und2XY81cwoWLGOqkpCIzNVxg==[/tex];[tex=14.143x7.929]TJe2CMZZhI3r8fE6n1csN7W8QRkDLDegUJ/FEgukguzW4xW/+N5DssLtG2cPwL+rhZN8sYTuRQ7AXDam6solxFIpiqTjgX3plHNsS0vPoNP7Br+YkOvEZGpRBv35h0JHdkPP+8LCr8DVPERQ5Zc3vdX5FbpDblOROcSJtuUHQ5osVssy37HRnCJbZmSnAFSkJbouFTGwPkbXCO0N7ke1UgqRV0vDCoB/xQagsCg4QxQY/lF8j+ngb5nJerJgFW1wG4GMOskclJAw8+A5kNUCMWVP/NKQQFASXXUNtYhmtAVWBqjBYTUwU0AcLBqL1Ivs3Hr0K8v3/xc0VVtqxlasjqteemPOT4PnCo/pN0V6jkQTQVsfUFddLVhrLWwx+7z+Cli8wwcTn8/+3FggNkVACeAkWDZSolppBGG2Sk1uQoGXqwCGjuQRanS509XHJnwrziCjFxJRP7PsGa6RFXsUrQ==[/tex][tex=15.5x5.786]Hv8biro46dFZr0nfb10df4IbXLDI8+GvikwEaQtR9la3DHWc50YzOVU//YQeyeKhyaggwLO8dy4ovJ1mM/dAXyiMO74QsgszwKki17LCdDQ1rA4cf++Y2/X79yNcyMJlZ4ZSLmB73OAbkM3eyF83L0acSmVI8X/Y69e/+MAyKN2Ipr6IE79oSU3y6gtfLXqDnCsAv8Zjoa/8Te9CKYra3FD36Y1zNIqdYJZxsDFH6AuUNwiHhN+5wDnHrfeXJqJvteHNf6MmKwHKwIVawdCa9P6jyN9OkiCIq1qYxUyTgRG+X7WB1juTYcIQKzRG8gAa[/tex];[tex=13.0x6.643]lcMWD2Jpi5XgoRTRW8nSqXLWKCC0hFzt7946s/Y0qMMCSCUYHikTbZazTkFVnp/umxblMznaO4p/G/rOCUyQWM1rUq7OfXRck0sHN85j19S6eBhnB6UdUIsomU6y1CpltZqa97lPZBrT+0lxaklDln8Hm5VX6x6ViZZDQT50lqCRLAV36fOqaJrBVvkzUZCHAC5gT95SmvfQ+aLOfb0/u4sABObFF9hgQqwtNFDWx8/CDK0yxFtW/PLfrzAWtVHopiVGZyt07regLjp4t0g5uazE1vJbrqBMqe5e3+zjMvTIgoW0IyckMHVA6JBjr2TpNgzEDKqkejY32A7m5VCkXQ==[/tex][tex=13.929x8.214]RTDpuAwSNdxaO1rmpYsI9DqPEGGPeGIU0lB7FDp8+jkEGpwqeiuOPcV4YuficTextKb80HpBXI+0imkARonxPmPwBdsIIwHqjPikSvOGGKciFqQDuWjN32uDISFqrUrq+UOKAzKYQiZaBqVB8XisFDO5FbAQRnxq9uKgvE//nmap59Tk8R8SMQnlRzJ8f0qn8hfsi1TisTiaVxUZRgpPOE+EKuPrix3P7RJZYP9fqY8f5jQ4uULBkjWhoZTj24fGZvEQazXsqrV7U5iUYSbK1Dmk8pG9bbYoCbBFyJSub8uNSc2fziRx3RX3moEGT5eYmnSShloFfE+W7r+HaIbuB1Que3FkGYfXzIveVzp8xb5QOfhWXx20o/TOIP/4mzEq[/tex]

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)

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