Please help with logic math Tanslate the following sentences

Please help with logic math.

Tanslate the following sentences into symbolic form using quantifiers and Negate each of the mathematical statements, putting your answers in positive form. Express each negation in natural, idiomatic english.

a) At least one British snake is poisonous. (All snakes)   b) At least one British snake is poisonous. (All animals) c) Not all precious stones are beautiful. (All stones) d) Every triangle is isosceles. (All geometric figures)   e) One of my friends does not have a car. (All people) f) If a man comes, all the women will leave. (All people)   f) All people are tall or short. (All people)   g) All people are tall or all tall people are short. (All people)   h) Some elephants do not like muffins. (All animals)   i) Everyone loves somebody. (All people)

Solution

At least one British snake is poisonous. (all snakes is the domain) Let S(x) be the statement that x is British and P(x) be the statement that x is poisonous: ?x(B(x) ? P(x)).(m) When the domain is all animals, we need the additional open sentence S(x) : x is a snake. Then we get ?x(S(x) ? B(x) ? P(x)).

(e)One of my friends does not have a car. (Note: This doesn