We introduce a language in which there are: - A constant me which represents the person who speaks, and a constant vegetables which represents the corresponding food; - Two symbols of binary relations eat and likes: eat(p, a) represents the property "p eat a " and likes(p, a) the fact that " p likes a ". 1. Give the logical formulas that correspond to the following expressions: (a) I like everything I eat. (b) There are things that I do not like but that I eat anyway. (c) Those who do not like vegetables eat nothing. (d) If everyone agrees to eat something he does not like then I eat vegetables.

Adding to more parts of same question: 7: f(i)≠f(i+1) for all i ∈ Z  set , number, statement or meaningless 8:{n∈Z: f(n)∈ AUBUC} set, number, statement or meaningless

(10) Let E denote the set of even integers, and O denote the set of odd integers. (a) Let P = "Every integer is either even or odd." Write P using logic symbols (and common notation for sets, like E, Z, N, Q etc).