Translate the following English sentences into symbolic sentences with quantifiers. The...

Translate the following English sentences into symbolic sentences with quantifiers.

The universe for each is given in parentheses.

(a) Not all precious stones are beautiful. (All stones)

(b) All precious stones are not beautiful. (All stones)

(c) Some isosceles triangle is a right triangle. (All triangles)

(d) No right triangle is isosceles. (All triangles)

(e) Every triangle that is not isosceles is a right triangle.

(f ) All people are honest or no one is honest. (All people)

(g) Some people are honest and some people are not honest. (All people)

(h) Every nonzero real number is positive or negative. (Real numbers)

(i) Every integer is greater than −4 or less than 6. (Real numbers)

(j) Every integer is greater than some integer. (Integers)

(k) No integer is greater than every other integer. (Integers)

(l) Between any integer and any larger integer, there is a real number. (Real numbers)

(m) There is a smallest positive integer. (Real numbers)

(n) No one loves everybody. (All people)

(o) Everybody loves someone. (All people)

(p) For every positive real number x, there is a unique real number y such that . (Real numbers)