updates
Sigma notation with minterms
I'm trying to understand what is meant by the notation $F(x,y,z)=\sum m(0,1,2,3)$ I found this webpage but it's still unclear to me. It states t...
Apr 14, 2026
Archive: Updates
updates
What are the differences between a claim, a statement and a proposition?
In logic, it seems like the words "claim", "statement" and "proposition" have the same meaning, i.e. a sentence which can be true or false (but not both),...
Apr 14, 2026
updates
Applying trigonometry in solving quintic polynomials?
So I came across the unsolvable quintic polynomial noticing that solutions can be found by connections with ellipses and such here. But more importantly, ...
Apr 14, 2026
updates
Verify a solution to a differential equations and determine the constants
Verify that the function $y(x)=C_1e^{-2x}+C_2e^x$ is a solution of the linear equation $\frac{d^2y}{dx^2}+\frac{dy}{dx}-2y=0$ for any choice of constants ...
Apr 14, 2026
updates
Are these statements true in the following sets?
I'd like to confirm my logic and better understand these statements. I'm supposed to find out if the following statements are true in $U = \Bbb ...
Apr 14, 2026
updates
Find the Vertices of an Ellipse Given Its Foci and Distance Between Vertices
I need to find the coordinates of two vertices with focal points of $(2, 6)$ and $(8, -2)$ and the distance between the vertices is $18$. I was able to ca...
Apr 14, 2026
updates
Multiset - double binomial coefficient?
In a recent question I have seen for the first time the symbol in my life: $$\left(\!\!{n\choose k}\!\!\right)$$ Practically why this symbol is used and w...
Apr 14, 2026
updates
Understanding "Divides" aka "|" as used logic
What are the rules for using the divides operator aka "$\mid$"? Is it false to say $2\mid5$ since $5/2$ = $2.5$ and $2.5\notin\mathbb{Z}$? Or does my ques...
Apr 14, 2026
updates
Given that $\sec \theta = k,\,|k| \ge 1$, express the following in terms of $k$
$\sec \theta = k,\,|k| \ge 1$ and that $\theta $ is obtuse, express in terms of $k$: (1) $\cos \theta $ (2) ${\tan ^2}\theta $ (3) $\cot \theta $ (4) $\cs...
Apr 14, 2026
updates
Soare's Definition of Recursive Enumeration
On page 33 and 34 of Soare's Recursively Enumerable Sets and Degrees he defined the recursive enumeration of an r.e. set $A$ to be a strong array of ...
Apr 14, 2026
