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A Privative Term signifies the absence of an attribute in a subject capable of possessing it, e.g. ‘unwise,’ ‘empty’. [Footnote: A privative term is usually defined to mean one which signifies the absence of an attribute where it was once possessed, or might have been expected to be present, e.g. ‘blind.’
Introduction. The purpose of this booklet is to give you a number of exercises on proposi-tional, first order and modal logics to complement the topics and exercises covered during the lectures of the course on mathematical logic.
1 Logical Equivalences. We have learned some logical equivalences. We say that two statements are logically equivalent when they evaluate to the same truth value for every assignment of truth values to their variables. So far we have seen: De Morgan’s Law :(p _ q) , (:p ^ :q) and :(p ^ q) , (:p _ :q) Implication law p ! q , :p _ q.
A proposition is any declarative statement that is true or false. The following symbols are called connectives and are used to stand for words. Truth functions for the connectives are defined as follows. P ∧ Q is true provided both P and Q are true.
PRACTICE EXERCISES. 1. Suppose p is the statement 'You need a credit card' and q is the statement 'I have a nickel.' Select the correct statement corresponding to the symbols ~(p∨q). You don't need a credit card and I have a nickel. It is not the case that either you need a credit card or I have a nickel.
Example. Let’s use real mathematical statements. Let’s consider the integers Z. Let x 2Z (x belongs to the set of integers) and the example we saw before. If x > 0 then x2 > 0. Rewrite this implication using sufficient, necessary, just if, and negations. • x > 0 is sufficient for x2 > 0. • x2 > 0 is necessary for x > 0. • x2 > 0, if ...
Exercise Sheet 1: Propositional Logic 1. Let p stand for the proposition“I bought a lottery ticket”and q for“I won the jackpot”. Express the following as natural English sentences: (a) ¬p (b) p∨ q (c) p∧ q (d) p ⇒ q (e) ¬p ⇒¬q (f) ¬p∨ (p∧ q) 2. Formalise the following in terms of atomic propositions r, b, and w, first ...
