MACM 101 Lecture 7: Lecture 7 Part 1_ Introduction Predicates and Quantifiers
21 Dec 2018
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Lecture 7 part 1: introduction predicates and quantifiers. We saw that some declarative sentences are not statements without specifying the value of. Some valid arguments cannot be expressed with all our machinery of tautologies, equivalences, and rules of inference. Sentences like x is greater than 3" or person x has a brother" are not true or false unless the variable is assigned some particular value. Sentence x is greater than 3" consists of 2 parts. The first part, x, is called the variable or the subject of the sentence. The second part the predicate, is greater than 3" refers to a property the subject can have. Sentences that have such structure are called open statements or predicates. We write p(x) to denote a predicate with variable x. X is a human being" contain 2 variables, binary predicates: q(x,y) Car x has colour y" contain 3 variables, ternary predicates: r(x,y,z) X is a son of y and z".
