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Concept · Sets & Inequalities
Sets and elements
membership (belongs-to / not-belongs-to)
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A Sets & Inequalities set, untimed
Nothing named here yet.
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Key formulas
12- UnionA ∪ B = { x : x ∈ A or x ∈ B }
- IntersectionA ∩ B = { x : x ∈ A and x ∈ B }
- Complement (relative to universe U)Ac = { x ∈ U : x ∉ A }
- DifferenceA − B = { x : x ∈ A and x ∉ B }
- Inclusion-exclusionn(A ∪ B) = n(A) + n(B) − n(A ∩ B)
- Subset count of an n-element set2n subsets2n − 1 proper subsets2n − 1 nonempty subsets
- Empty set ∅ is a subset of every set
- Quadratic inequality ax2+bx+c>0solution keyed to root(s) and sign of a / discriminant Δ=b2−4ac (Δ>0 two roots, Δ=0 one, Δ<0 none)
- Roots straddle k (one >k, one <k) for a>0f(k) < 0
- Rational inequality f(x)/g(x) ≤ 0sign chart on numerator/denominator zeros (g(x) ≠ 0)
- Absolute value|x − a| < b ⇔ a − b < x < a + b (b>0)
- Inequality multiplicative propertymultiplying/dividing by a negative reverses the inequality
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsAlgebra 2 foundations