Let p(x)= x3+(5m+1)x+5n+1, where m,n are integers. Which of the following statements is not true?( )
A: Q[x]/ is field.
B: p(x) is irreducible over Q[x]
C: x+ has multiplicative inverse in Q[x]/.
D: Q[x]/ is an integer domain but not a field
A: Q[x]/ is field.
B: p(x) is irreducible over Q[x]
C: x+ has multiplicative inverse in Q[x]/.
D: Q[x]/ is an integer domain but not a field
举一反三
- ( )不是有效的推理。 A: 前提：("x)(H(x)ÞM(x)) 结论：("x)("y)(H(y)∧N(x, y))Þ($y)(M(y)∧N(a, y)) B: 前提：("x)(G(x)ÞH(x))，~($x)(F(x)∧H(x)) 结论：($x)F(x)Þ($x)G(x) C: 前提：("x)(P(x)ÞQ) 结论：("x)P(x)ÞQ D: 前提：("x)P(x)∨("x)Q(x) 结论：("x)(P(x)∨Q(x))
- ( )不是有效的推理。 A: 前提：("x)(~P(x)ÞQ(x)), ("x)~Q(x)结论：P(a) B: 前提：("x)(P(x)ÞQ) 结论：("x)P(x)ÞQ C: 前提：("x)(P(x)∨Q(x)), ("x)(Q(x)Þ~R(x)) 结论：($x)(R(x)ÞP(x)) D: 前提：("x)(P(x)Þ(Q(x)∧R(x))), ($x)(P(x)∧S(x))结论：("x)(R(x)∧S(x)) E: 前提：("x)($y)P(x, y)结论：("x)($y)($z)(P(x, y)∧P(y, z)) F: 前提：("x)P(x)∨("x)Q(x)结论：("x)(P(x)∨Q(x)) G: 前提：("x)(G(x)ÞH(x))，~($x)(F(x)∧H(x))结论：($x)F(x)Þ($x)G(x) H: 前提：("x)(H(x)ÞM(x))结论：("x)("y)(H(y)∧N(x, y)) Þ ($y)(M(y)∧N(a, y) )
- 在指定的解释下，下列公式为真的是() A: ("x)(P(x)∨Q(x)),P(x):x=1,Q(x):x=2,论域:{1,2} B: ($x)(P(x)∧Q(x)),P(x):x=1,Q(x):x=2,论域: {1,2} C: ($x)(P(x) →Q(x)),P(x):x>2,Q(x):x=0,论域:{3,4} D: ("x)(P(x)→Q(x)),P(x):x>2,Q(x):x=0,论域:{3,4}
- 以下谓词公式中，( )不是逻辑有效式。 A: ($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))