Notes: Evaluating Functions
... What is f (2) ? --------------------------------------------------------------------------------------------------------------------Let function g be represented by the following list of ordered pairs: {(0,1), (5, 7), (10,12)} . What is a shorter notation for "the output of function g when the inpu ...
... What is f (2) ? --------------------------------------------------------------------------------------------------------------------Let function g be represented by the following list of ordered pairs: {(0,1), (5, 7), (10,12)} . What is a shorter notation for "the output of function g when the inpu ...
A simplified form of condensed detachment - Research Online
... (m.g.u) of a and ft if every other unification of a and /? is a substitution instance ofa(a). A substitution a is said to be alphabetic*relative to a formula a, if it replaces all or some of the variables in a by variablesdistinct from each other and from any variables in a that are not replaced. N ...
... (m.g.u) of a and ft if every other unification of a and /? is a substitution instance ofa(a). A substitution a is said to be alphabetic*relative to a formula a, if it replaces all or some of the variables in a by variablesdistinct from each other and from any variables in a that are not replaced. N ...
Logic and Automata - Cheriton School of Computer Science
... Theorem. A set of integers is definable in Th(N, +, Vk ) if and only if its characteristic sequence is k-automatic. Proof. First we show how to construct a finite automaton Mϕ corresponding to any formula ϕ of Th(N, +, Vk ). The idea again is that Mϕ will accept the base-k representations of all n-t ...
... Theorem. A set of integers is definable in Th(N, +, Vk ) if and only if its characteristic sequence is k-automatic. Proof. First we show how to construct a finite automaton Mϕ corresponding to any formula ϕ of Th(N, +, Vk ). The idea again is that Mϕ will accept the base-k representations of all n-t ...
Notes for 3.6 Variation (pp. 368 – 372)
... then there is a direct variation. That ratio is called the constant of proportionality. These problems always fall into a pattern: there is one sentence that has a complete fact relating the values of the story, and there is one sentence with incomplete information that you must complete. This sets ...
... then there is a direct variation. That ratio is called the constant of proportionality. These problems always fall into a pattern: there is one sentence that has a complete fact relating the values of the story, and there is one sentence with incomplete information that you must complete. This sets ...
Objective – To use tables to represent functions.
... Objective – To use tables to represent functions. A relation is a function if for each input there is EXACTLY one output. Input-Output Table (Function Table) ...
... Objective – To use tables to represent functions. A relation is a function if for each input there is EXACTLY one output. Input-Output Table (Function Table) ...
engr_123_matlab_lab6
... (assuming the file exists) diary labsession.txt Saves a copy of the subsequent text that appears in the Command Window (input/output) as a text file called labsession.txt. If the labsession.txt file already exists, the diary command will append or add on to the end of the file. Note: The diary comma ...
... (assuming the file exists) diary labsession.txt Saves a copy of the subsequent text that appears in the Command Window (input/output) as a text file called labsession.txt. If the labsession.txt file already exists, the diary command will append or add on to the end of the file. Note: The diary comma ...
2.1 Functions and their Graphs
... determine if a relation is a function. • Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. • If there are not two points on the same vertical line then the relation is a function. • If there are two points on the same vertical line then the rel ...
... determine if a relation is a function. • Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. • If there are not two points on the same vertical line then the relation is a function. • If there are two points on the same vertical line then the rel ...
Do Now 9/7/07
... Do Now 9/8/10 Take out HW from last night. – Text p. 7-8, #12-30 evens, #42-48 evens ...
... Do Now 9/8/10 Take out HW from last night. – Text p. 7-8, #12-30 evens, #42-48 evens ...
Lec10.pdf
... SOSCs — (1) diminishing marginal returns to each input, (2) diminishing returns to scale (this is not fully rigorous) Result - (unconditional) input demand functions L∗ (p, w, r), K ∗ (p, w, r), yielding Q∗ = F (K ∗ , L∗ ) Substitute in profit expression to get “dual” profit function Π∗ (p, w, r) = ...
... SOSCs — (1) diminishing marginal returns to each input, (2) diminishing returns to scale (this is not fully rigorous) Result - (unconditional) input demand functions L∗ (p, w, r), K ∗ (p, w, r), yielding Q∗ = F (K ∗ , L∗ ) Substitute in profit expression to get “dual” profit function Π∗ (p, w, r) = ...
monadic second order logic
... Formulas are interpreted over N0 Individual variables x,y,..are interpreted as natural numbers ie. elements of N0 Function Successor corresponding to adding one t t’ is true provided t and t’ denote the same natural number ...
... Formulas are interpreted over N0 Individual variables x,y,..are interpreted as natural numbers ie. elements of N0 Function Successor corresponding to adding one t t’ is true provided t and t’ denote the same natural number ...
Harvard University
... • A proposition P is like a boolean variable. Its value is either “true” or “false.” • A predicate P (x) is like a boolean-valued function. It may have the value “true” for some values of the x and the value “false” for others. • A predicate can have more than one argument; e.g. Enrolled(x, y) might ...
... • A proposition P is like a boolean variable. Its value is either “true” or “false.” • A predicate P (x) is like a boolean-valued function. It may have the value “true” for some values of the x and the value “false” for others. • A predicate can have more than one argument; e.g. Enrolled(x, y) might ...
Digital Logic and the Control Unit
... functional representation. Note that F2 is 1 if and only if two of X, Y, and Z are 1. Given this, we can give a functional description of the function as F2 = XY + XZ + YZ. As the student might suspect, neither the pattern of 0’s and 1’s for F1 nor that for F2 were arbitrarily selected. The real ...
... functional representation. Note that F2 is 1 if and only if two of X, Y, and Z are 1. Given this, we can give a functional description of the function as F2 = XY + XZ + YZ. As the student might suspect, neither the pattern of 0’s and 1’s for F1 nor that for F2 were arbitrarily selected. The real ...
Algebra 1
... The Vertical Line Test is a quick way to help you determine if a relation is a function. If all possible vertical lines cross the graph once or not at all, then the graph represents a function. The graph does not represent a function if you can draw even one vertical line that crosses the graph two ...
... The Vertical Line Test is a quick way to help you determine if a relation is a function. If all possible vertical lines cross the graph once or not at all, then the graph represents a function. The graph does not represent a function if you can draw even one vertical line that crosses the graph two ...
Algebra I
... Write Algebraic Expressions for These Word Phrases • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number ...
... Write Algebraic Expressions for These Word Phrases • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number ...
Algebra I
... Write Algebraic Expressions for These Word Phrases • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number ...
... Write Algebraic Expressions for These Word Phrases • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number ...
2.1 Functions and their Graphs
... determine if a relation is a function. • Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. • If there are not two points on the same vertical line then the relation is a function. • If there are two points on the same vertical line then the rel ...
... determine if a relation is a function. • Slide any vertical line (pencil) across the graph to see if any two points lie on the same vertical line. • If there are not two points on the same vertical line then the relation is a function. • If there are two points on the same vertical line then the rel ...
Exercises for CS3511 Week 31 (first week of practical)
... functionally complete set of connectives. Making use of this result, can you prove that {NAND} is also functionally complete? Answer: the reasoning is similar to that in 4a, but it may be a bit trickier to find the right formulas: p can be expressed as p p|p. (It helps to do negation before conj ...
... functionally complete set of connectives. Making use of this result, can you prove that {NAND} is also functionally complete? Answer: the reasoning is similar to that in 4a, but it may be a bit trickier to find the right formulas: p can be expressed as p p|p. (It helps to do negation before conj ...
Function Identification PowerPoint
... any two points lie on the same vertical line. If there are not two points on the same vertical line then the relation is a function. If there are two points on the same vertical line then the relation is NOT a function ...
... any two points lie on the same vertical line. If there are not two points on the same vertical line then the relation is a function. If there are two points on the same vertical line then the relation is NOT a function ...