According to the first premise, all items that are classified as apples are also classified as fruits. According to the second premise, Granny Smith is classified as an apple. The first premise is a general statement, while the second premise refers to a specific case. The conclusion says that a Granny Smith has to be a fruit because of its inherent properties as an apple. This deductive argument is also valid , which means that the conclusion necessarily follows from the premises. So, does a valid deductive argument mean that the premises and conclusions are true? Suppose I formed this deductive argument:

I would say that the applicant who wrote the “Imagine” essay didn’t get due to the essay’s flat prose, poor organization, and questionable grammar, not its subject matter. The song was not sung “by the show,” but by the characters on the show. The sentence “When I watched this episode while the deaf adolescents were singing it, and soon joined by another glee club, it surprisingly affected me…” is just an incredible mess. He didn’t watch “while” they were singing; it should be “were joined by;” and “surprisingly affected me” is a terribly clumsy construction. How about: “As I watched another glee club join the deaf adolescents in singing the song during this episode, I was surprised by how much it affected me.” Not all applicants will be strong writers, but all need to show at least a basic grasp of how to communicate a thought.

I was extremely stressed out about writing my personal statement, and finally decided to search the internet for advice and assistance. I came across the personal statement editing service on the PA Life , and decided to give it a try. I received a response within a day, and my stress was instantly relieved. I worked personally with Duke to edit my statement, and he is a phenomenal writer. He didn’t change the content of my statement, but rather helped me tell my story in a way that is much more desirable! I cannot recommend this service enough to others seeking help on their personal statement. Duke was friendly, sincere, and definitely experienced! I felt 100% confident in his editing abilities, and we worked together the entire time so that we were both pleased with the results! Thanks again, Duke, for all of your help!

Let BS be perpendicular to HG, and let HB be drawn; also put the radius AO $=a$, OH $=b$, AH $(b-a)=c$, H$n = y$ and HB $=c+x$; then A$n = y-c$, G$n=2a-y+c$, and consequently $\overline{y-c}\times \overline{2a-y+c}~ (=~$A$n~\times$ G$n =~$B$n^2 =~$BH$^2-$H$n^2) = \overline{c+x}^2 -y^2$. From which Equation we get $\displaystyle{ y=\frac{2ac+2c^2+2cx+x^2}{2a+2c}}$ (because $a+c=b$.) Whence also $\displaystyle{ 2p\times \overline{1-\frac{Hn}{HB}}= 2p\times \overline{1-\frac{2bc+2cx+x^2}{2b\times\overline{c+x}}}}$: Which multiply'd by $\displaystyle{\frac{c\dot{x}+x\dot{x}}{b}=\dot{y}}$ gives $\displaystyle{\frac{p\times\overline{2ax\dot{x}-x^2\dot{x}}}{b^2}}$ for the Fluxion of the required Force; whereof the Fluent $\displaystyle{\frac{p\times\overline{ax^2-\frac{1}{3}x^3}}{b^2}}$ will be the Attraction of the Segment ABS: Which therefore, when B coincides with G and $x$ is $=2a$, becomes $\displaystyle{\frac{4pa^3}{3b^2}}$, for the Measure of the Attraction of the whole Sphere. .

Let BS be perpendicular to HG, and let HB be drawn; also put the radius AO $=a$, OH $=b$, AH $(b-a)=c$, H$n = y$ and HB $=c+x$; then A$n = y-c$, G$n=2a-y+c$, and consequently $\overline{y-c}\times \overline{2a-y+c}~ (=~$A$n~\times$ G$n =~$B$n^2 =~$BH$^2-$H$n^2) = \overline{c+x}^2 -y^2$. From which Equation we get $\displaystyle{ y=\frac{2ac+2c^2+2cx+x^2}{2a+2c}}$ (because $a+c=b$.) Whence also $\displaystyle{ 2p\times \overline{1-\frac{Hn}{HB}}= 2p\times \overline{1-\frac{2bc+2cx+x^2}{2b\times\overline{c+x}}}}$: Which multiply'd by $\displaystyle{\frac{c\dot{x}+x\dot{x}}{b}=\dot{y}}$ gives $\displaystyle{\frac{p\times\overline{2ax\dot{x}-x^2\dot{x}}}{b^2}}$ for the Fluxion of the required Force; whereof the Fluent $\displaystyle{\frac{p\times\overline{ax^2-\frac{1}{3}x^3}}{b^2}}$ will be the Attraction of the Segment ABS: Which therefore, when B coincides with G and $x$ is $=2a$, becomes $\displaystyle{\frac{4pa^3}{3b^2}}$, for the Measure of the Attraction of the whole Sphere. .