MATH 1190 Lecture Notes - Lecture 6: Propositional Function, Existential Quantification, Universal Quantification

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1190
• Professor: Laura Colmenarejo Hernando

Document Summary

Math 1190 lecture 6 notes- preconditions and post-conditions. P(x) is not always true when x is in the domain. Xq(x), where the domain consists of all real numbers: solution: q(x) is not true for every real number x, because, for instance, q (3) is false, that is, x = 3 is a counterexample for the statement xq(x). , xn it follows that the universal quantification xp(x) is the same as the conjunction. P(x1) p(x2) p(xn), because this conjunction is true if and only if p(x1), P(3) p(4), because the domain consists of the integers 1, 2, 3, and 4: because p (4), which is the statement 42 < 10, is false, it follows that. Note that x2 x if and only if x2 x = x(x 1) : consequently, x2 x if and only if x 0 or x 1.