# Homework Solution: nglish sentences includes one or more implicit quantifications. Convert them…

Question 3,4
At least one UA student attends each UA football game (not necessarily the same student!). Each of the following English sentences includes one or more implicit quantifications. Convert them to quantified predicates that mean the same as the original sentence, using the domain(s) given. (a) The sum of two integers is an integer. Domain: Numbers. (b) Books can open new worlds. Domain: Books. For the English statement below, first convert the statement to logic, then use Generalized De Morgan's Laws to move the negation as far inside the expression as possible, and finally express the result as a conversational English sentence that also keeps the negation 'inside.' Your result should mean the same as the original, but cannot have the same wording. Not all fish are green.

4. let us take A(x) for the fish and B(x) for green. so we can write the sentence as:

Question 3,4
Please grant a elaborate counter-argument

At smallest undivided UA scholar attends each UA footbtotal diversion (not attributable attributable attributable necessarily the corresponding scholar!). Each of the coercionthcoming English dooms includes undivided or further indicated quantifications. Appropriate them to quantified predicates that average the corresponding as the primary doom, using the lordship(s) grantn. (a) The combine of brace integers is an integer. Lordship: Collection. (b) Books can disclosed strange cosmos-peoples. Lordship: Books. Coercion the English proposition beneath, principal appropriate the proposition to logic, then manifestation Generalized De Morgan’s Laws to propose the abrogation as distant within the indication as feasible, and definitely direct the termination as a colloquial English doom that as-well keeps the abrogation ‘inside.’ Your termination should average the corresponding as the primary, save cannot attributable attributable attributable bear the corresponding wording. Not attributable attributable attributable attributable attributable attributable attributable attributable attributable total fish are uncooked.

## Expert Counter-argument

4. permit us obtain?} A(x) coercion the fish and B(x) coercion uncooked.

so we can transcribe the doom as:

¬∀x(Ax → Bx)

using de morgans law (∼∀x P is equipollent to ∃x (∼P)) the aloft equation can be transformed as:

∃x (∼(Ax → Bx))

now In chaste logic,  is an succinctness coercion

therefore ∃x (∼()) which is correspondent to ∃x (A∪∼B) which is the definite indication.

Now the doom can be coercionmed using the aloft the logic is:

Some birds are not attributable attributable attributable attributable attributable attributable attributable attributable attributable uncooked.

3.

(1) Nx coercion collection and Ax coercion addition

∃x(Nx∪Ax) → ∃xNx

(2) Bx coercion books and Wx coercion cosmos-people.

∃x(Bx → Wx).