Prove: (a) The triple ('P(}), A, ) is a vector space over 4'2. (b) The line complements, together with the empty set, form a subspace of (730:), A, ) . (c) For any S g F, the sum of S with the entire set is equal to the complement of S inside F. (d) The set \"H containing the Fano lines, their complements, the entire set .7: and the empty set '3 is also a linear subspace of (730:), A, ). (e) Any two distinct elements of 'H differ in at least three elements. Here a some criteria for quality writing: - Is the argument logically correct and complete? - Does the author write in full sentences, and are these grammatically correct? . ls each symbol introduced before it is referenced? - Are pronouns used sparingly, and is it always absolutely clear what any given pronoun refers to? - Does the logical argument ow in the correct direction, i.e. does the text start by assuming statements that are known and continue to deduce what needs to be proved? - If the text begins by stating what needs to be shown and reduces this to a statement we already know to be true, is this very clearly explained at each step; if implication arrow are used, do these point in the correct direction? (Try to avoid the three dots for "therefore" -- they can be used correctly, but more often than not they indicate that the student didn't think about which logical symbol is the correct one.) - How easy or difcult is it to follow the exposition