Oxford University (OX)

Set Difference A - B, the set containing those elements that are in A but not in B Set Symmetric Difference A ⊕ B: the set of elements that are a member of exactly one of A and B, but not both. An alternative definition of the symmetric difference operation is: A ⊕ B = ( A - B ) ∪ ( B - A ) Set Complement the set of all elements in U that are not elements of A. An alternative definition of A is U - A. Set Intersection A ∩ B: the resulting set that contains...

diagonal matrix square matrix which all non-diagonal entries are 0 diagonal entries can be 0 identity matrix diagonal matrix which all entries along main diagonal is 1, all other entries = 0 can different sized matrices be added? no matrix addition [3|-4] + [-2|8] [1|0] + [-5|-3] = [3+-2|-4+8] [1+-5|0+-3] = [1|4] [-4|-3] scalar refers to real numbers ex_ 3, -5.1, π scalar multiple each entry is multiplied by scalar multiplying mat...

Form When an argument has been translated from English using symbols Invalid Describes an argument when the conclusion is false in a situation with all the hypotheses are are true Valid Describes an argument when the conclusion is true whenever the hypotheses are all true Conclusion The final proposition Hypothesis Each of the propositions within an argument Argument Sequence of propositions Two Player Game In reasoning whether a quantified statem...

boolean complement denoted with bar symbol reverses elements value (bar over)0=1 (bar over)1=0 boolean addition 0+0=0 0+1=1 1+0=1 1+1=1 boolean multiplication 0×0=0 0×1=0 1×0=0 1×1=1 ⊕ exclusive or XOR outputs 1 only when inputs are different 0⊕0=0 1⊕0=1 0⊕1=1 1⊕1=0 idempotent of boolean x+x=? x*x=? x+x=x x*x=x associative of boolean (x+y)+z=? (xy)z=? (x+y)+z=x+(y+z) (xy)z=x(yz) commutative of boolean x...

p∧q conjunction "and" T/T=T T/F=F F/T=F F/F=F p∨q disjunction/inclusive or "or" T/T=T T/F=T F/T=T F/F=F p⊕q exclusive or "or" T/T=F T/F=T F/T=T F/F=F ¬p negation "not" ¬T = F ¬F = T p→q conditional operation "if p then q" T/T=T T/F=F F/T=T (p=F, q=T regardless of truth value) F/F=T converse of p→q q→p contrapositive of p→q ¬q→¬p inverse of p→q ¬p→¬q p↔q bicondi...

What is the notation for subset? ⊆ A collection of objects is known as a set What is the notation for integers? ℤ What is the notation for element? ∈ What is the notation for set-roster? { } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0} T/F: Order matters in ordered pair...

Why are capital structure considerations relevant for LBOs? The nature of LBOs is to rely heavily on leverage to produce attractive returns to equity investors. What is a primary pitfall to leverage? Creates investment risk and could jeopardize an equity holder's ability to recoup his/her initial investment. Choosing the _________________ ______________ ________________ is extremely important and will influence how the target company runs its operations? Optimal capital structu...

Debt Schedule Beginning Balance Plus: PIK Interest (Calculated on Beginning Balance) Plus: Recap Debt / Additional Allocation Less: Mandatory Repmt Less: Voluntary Repmt Ending Balance Interest Expense = Average Btw Beginning & Ending Balance The Revolver Inputs Maximum Capacity: maximum amount a revolver can be drawn -any borrowing cannot exceed this amount Interest Rate Rate + MAX(LIBOR, Rate Floor) Optional Borrowing =Min(Available Capacity, -MIN(Cash Available ...

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exposition character-painter lady, narrator, lou, morris twins setting-south corner of taliaterro street and fifth inciting incident painter lady paints on the wall rising action tell painter lady all about the wall. morris twins bring the P.L. "suppah". P.L. goes to the resterant. mama scolds her for being picky/not to elters. Lou and narrator decide to graffitti the wall. climax block party atn the wall lou and narrator see painting and realizes it represents the her...