命题“∃(x,y),x,y∈R,2x+3y+3<0”的否定是( )A.∃(x,y),x,y∈R,2x+3y+3<0B.∃(x,y),x,y∈R,2x+3y+3
题型:肇庆一模难度:来源:
命题“∃(x,y),x,y∈R,2x+3y+3<0”的否定是( )A.∃(x,y),x,y∈R,2x+3y+3<0 | B.∃(x,y),x,y∈R,2x+3y+3≥0 | C.∀(x,y),x∈R,y∈R,2x+3y+3≥0 | D.∀(x,y),x∈R,y∈R,2x+3y+3>0 |
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答案
命题“∃(x,y),x,y∈R,2x+3y+3<0”的否定是:∀(x,y),2x+3y+3≥0. 故选C. |
举一反三
下列命题中,真命题是( )A.∀x∈R,x2-x-1>0 | B.∀α,β∈R,sin(α+β)<sinα+sinβ | C.函数y=2sin(x+)的图象的一条对称轴是x=π | D.∃α,β∈R,sin(α+β)=cosα+cosβ |
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命题“∀a∈Q,≥a”的否定是( )A.∀a∉Q,≥a | B.∃a∈Q,<a | C.∃a∈Q,≥a | D.∀a∉Q,<a |
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已知命题p:∀x1,x2∈R,(f(x2)-f(x1))(x2-x1)≥0,则¬p是( )A.∃x1,x2∈R,(f(x2)-f(x1))(x2-x1)≤0 | B.∀x1,x2∈R,(f(x2)-f(x1))(x2-x1)≤0 | C.∃x1,x2∈R,(f(x2)-f(x1))(x2-x1)<0 | D.∀x1,x2∈R,(f(x2)-f(x1))(x2-x1)<0 |
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若命题p为:∃x∈R,2x≤0,则命题¬p为( )A.∀x∈R,2x≤0 | B.∃x∈R,2x>0 | C.∃x∈R,2x≤0 | D.∀x∈R,2x>0 |
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