QC(QC) Is not a vector space, where Qis the set of irrational numbers because 

1
α + (β + c) = α + (β + c) for all α, β and c ∈ Qc 
2
u + v ∈ Q for all u, v ∈ Qc
3
α.1 = 1.α = α for all α ∈ Qc
4
None of these 

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