Are my answers true or wrong or not even wrong?
Exercises says translate the following english sentences into symbolic sentences with quantifiers quantifiers the universe for each is given in parentheses (there's no problem if i just wrote an equivalent statement and not the exact model in which the statement is written see the comments)
(a) Not all precious stones are beautiful. (All Stones)
Old answer: $$\text{$(\exists x)$$($$x$ is precious $\wedge$ $x$ isn't beautiful$)$}$$ New answer: $$\neg(\forall x)(\text{$x$ is precious $\implies$ $x$ is beautiful})$$
(b) All precious stones are not beautiful. (All Stones)
Old answer: $$\text{$(\forall x)$$($$x$ is precious $\implies$ $x$ isn't beautiful$)$}$$ New answer: $$\text{$(\forall x)$$($$x$ is precious $\implies$ $\neg$($x$ is beautiful)$)$}$$
(c) Some isosceles triangle is a right triangle. (All Triangles)
Old answer = New answer: $$\text{$(\exists x)$$($$x$ is isosceles $\wedge$ $x$ is right$)$}$$
(d) No right triangle is isosceles. (All Triangles)
Old answer: $$\text{$(\forall x)$$($$x$ is right $\implies$ $x$ isn't isosceles$)$}$$ New answer: $$\text{$\neg(\exists x)$$($$x$ is right $\wedge$ $x$ is isosceles$)$}$$
(e) All people are honest or no one is honest (All People)
Old answer: $$\text{$(\forall x)$$($$x$ is honest$)$ $\vee$ $(\forall y)(y$ isn't honest$)$}$$ New answer: $$\text{$(\forall x)$$($$x$ is honest$)$ $\vee$ $\neg(\exists y)(y$ is honest$)$}$$
(f) Some people are honest and some people are not honest. (All People)
Old answer: $$\text{$(\exists x)(x$ is honest$)$ $\wedge$ $(\exists x)(x$ isn't honest$)$}$$ New answer: $$\text{$(\exists x)(x$ is honest$)$ $\wedge$ $(\exists x)(\neg(x$ is honest$))$}$$
(g) Every nonzero real number is positive or negative. (Real Numbers)
Old answer = New answer: $$\text{$(\forall x)(x\neq0$ $\implies$ $x\gt0$ $\vee$ $x\lt0$$)$}$$
(h) Every integer is greater than -4 or less than 6. (Real Numbers)
Old answer = New answer: $$\text{$(\forall x)(x\in\mathbb{Z}$ $\implies$ $x\gt-4$ $\vee$ $x\lt6$$)$}$$
(i) Every integer is greater than some integer. (Integers)
Old answer = New answer: $$\text{$(\forall x)(\exists y)($$x\gt y$$)$}$$
(j) No integer is greater than every other integer. (Integers)
Old answer: $$\text{$(\forall x)(\exists y)(x\le y)$}$$ New answer: $$\text{$\neg(\exists x)(\forall y)(x\gt y)$}$$
(k) Between any integer and any larger integer, there is a real number. (Real Numbers)
Old answer = New answer: $$\text{$(\forall x)$$(\forall y)$$[$$x\in\mathbb{Z}$ $\wedge$ $y\in\mathbb{Z}$ $\wedge$ $x\gt y$ $\implies$ $(\exists z)$$($$x\gt z\gt y$$)$$]$}$$
(l) There is a smallest positive integer. (Real Numbers)
Old answer = New answer: $$\text{$(\exists x)$$(\forall y)$$($$x\gt0$ $\wedge$ $x\in\mathbb{Z}$ $\wedge$ $y\in\mathbb{Z}$ $\wedge$ $y\gt0$ $\wedge$ $x\ne y$ $\implies$ $x\lt y$ $)$}$$
(m) No one loves everybody. (All People)
Old answer: $$\text{$(\forall x)$$(\exists y)$$($$x$ doesn't love $y$$)$}$$ New answer: $$\text{$\neg(\exists x)$$(\forall y)$$($$x$ loves $y$$)$}$$
(n) Everybody loves someone. (All People)
Old answer = New answer: $$\text{$(\forall x)$$(\exists y)$$($$x$ loves $y$$)$}$$
(o) For every positive real number $x$ there is a unique real number $y$ such that $2^y=x$. (Real Numbers)
Old answer = New answer: $$\text{$(\forall x)$$(\exists!y)$$($$x=2^y$$)$}$$
Also side question do you think that with lots of efforts with hours of practice like these exercises i can get better and with 400000 hours of practice i can be the best in a domain? Thnx =) =) And sorry for my bad english :/