Wykaż, że zbiór A\B jest zbiorem jednoelementowym, jeżeli:
A = { x : x² ( x ²-16) ≥ 0}
B = { x :|x| > 3 }, gdzie x∈R
A
x² ( x ²-16) ≥ 0
x=0 ∨ x=-4 ∨ x=4
x∈<-∞,-4>u{0}u<4,∞) ⇐ rys1
B|x|>3
x>3 ∨ x<-3
x∈(-∞,-3)u(3,∞)
(<-∞,-4>u{0}u<4,∞))\((-∞,-3)u(3,∞))=0 ⇐ rys2
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A
x² ( x ²-16) ≥ 0
x=0 ∨ x=-4 ∨ x=4
x∈<-∞,-4>u{0}u<4,∞) ⇐ rys1
B
|x|>3
x>3 ∨ x<-3
x∈(-∞,-3)u(3,∞)
(<-∞,-4>u{0}u<4,∞))\((-∞,-3)u(3,∞))=0 ⇐ rys2