Discrete_math.docx - Discrete math Exercise A Write down in...

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Discrete math Exercise A Write down, in your own words, a detailed specification for a library loans and returns record system You are required to: (i) Fully specify your systems using propositions and predicates (ii) Test the validity of a simple propositional clause, relevant to the library by constructing a truth table Exercise B For each of these binary relations, determine whether they are reflexive/irreflexive, symmetric/antisymmetric or transitive. Give reasons for your answers and state whether or not they form order relations or equivalence relations. 1. On the set {alf, bert, tom}, the relation {(alf,alf), (alf, bert), (bert, bert), (tom,tom) }. 2. Take E to be the set of all arithmetic expressions involving variables such as x, y, z, For example, “x +3y” is an expression belonging to E. The binary relation on E contains all pairs of expressions, (exp1, exp2), which give same result for all values of their variables. For example, the pair of expressions (“x+3y”, “y+x+2y”) is in the relation because they have the same values for all values of x and y. But (“x+3y”, “x”) does not belong to the relation as the expressions have different values when x=1 and y=1, say. For the following question, state the relation and explain your reasoning. 3. Let W be the set of days in the week {Sun, Mon, Tue, Wed, Thu, Fri, Sat}. What relation, as a subset
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