EECS 1019 Study Guide - Midterm Guide: Irrational Number, Contraposition, Rational Number

• School: York University
• Department: Electrical Engineering and Computer Science
• Course: EECS 1019
• Professor: Suprakash Datta

Document Summary

Instructor: s. datta: (6 points) let g : z z z z be de ned by g(x, y) = (x + y, 3y). Recall that to prove that a function is injective, we must show that if f (x, y) = f (z, w) then (x, y) = (z, w). The function is not onto because it will not produce any pair whose second number is not a multiple of 3, e. g. (1, 1): (2+2 points) write down the following statement in predicate logic (using quanti ers). Then write down the negation of the predicate logic expression. Use the domain r and de ne a predicate isrational(x) appropriately. The product of two irrational numbers may be rational. X y( isrational(x) isrational(y) isrational(x y): (3 points) prove or disprove: if x is an irrational number, then 3 x is an irrational number. Solution: the easiest approach is proving the contrapositive.