Functions: Mapping

For the functions f defined below, determine which are 1:1, onto or both. 1) f: R onto R, f(x) = |x| 2) f: R onto R, f(x) = x^2 + 3 3) f: R onto R, f(x) = x^3 + 3 4) f: R onto R, f(x) = x(x^2-4) 5) f: R onto R, f(x) = |x| + x 6) f: N onto N, f(x) = x + 1 7) f: N onto NxN, f(x) = (x,x) 8) f: NxN onto N, f( ...continues

Symbolic Logic Problem

I have to determine whether or not this formal argument below is valid. If it is I have to provide a derivation of the conclusion from the premises, which I don't know how to do. If it is invalid, an interpretation which shows the invalidity must be constructed. The & signs mean "and" usually signified by a dot. The asterisk ...continues

Symbolic Logic Problem

I need to know how to construct a formal proof which shows that the sentence below is a theorem of predicate logic. The ^ sign indicates the word "or". The asterics indicates a conditional usually indicated by an arrow. No quantifier negation rules can be used. [(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY] * (~(EX)RX ^ (Z)(EY)SZY)

Symbolic Logic : Predicate Logic

The asterisk implies a conditional usually indicated by an arrow. The & sign indicates "and". In Aristotelian logic (X)(FX*GX) logically implies (EX)(FX & GX). Is this true in predicate logic? If not, why not?

Symbolic Logic : Predicate Logic

The sentence below is a theorem of predicate logic. Show that it is by deriving it from the null set of premises. If any "individual" in the domain has a property, then every individual has it. I need help explaining this and with the derivation. (EX)(FX --->(Y)FY)

Symbolic Logic : Symbolic Notation

Determine whether or not the argument below is valid. Transcribe it into symbolic notation and if it is valid, provide a derivation of the conclusion from the premises using only primitive rules of inference. The area of a triangle is the area of a three sided figure. Since triangles are three sided.

Symbolic Logic Problem

Use the method of truth table expansion to determine whether or not the sentence below is a theorem of quantified logic. The # indicates a biconditional, usually indicated by a double arrow. (EX)(Y)FXY#(Y)(EX)FXY

Real Analysis :Problem Prove a function is integrable over [a,b]

Let f:[a,b] mapped to the Reals be a function that is integrable over [a,b], and let g:[a,b] mapped to the Reals be a function that agrees with f except at two points. Prove g is integrable over [a,b].

Budget Pie Graph: How to Handle a Deficit

We have to make a pie graph of a budget. The problem is the expenditure exceed the income. This is what the teacher wanted. My problem is how do you compose a pie graph when instead of 100% the expenditures are 131% OF THE INCOME. I know how to compute the angles and everything but thereare only 360 degrees in the circle. We hav ...continues

Symbolic Logic Problem : Sentence to Expression

Transcribe the English argument below into an appropriate logical language adequate to determine it to be valid. Also, please provide a derivation of the conclusion from the premises within the same logical system (by which you transcribed it). *this seems to be predicate logic and probably requires universal and existential q ...continues