MAT102H5 Study Guide - Midterm Guide: Quadratic Equation, Contraposition

• School: UTM
• Department: Mathematics
• Course: MAT102H5
• Professor: Marina Tvalavadze

Document Summary

Mat102 - intro. to mathematical proofs - winter 2016 - utm. Term test (version a) - october 20, 2016 - solutions. R = ( x r) ((|x 1| 2 ) (x z)) (cid:0) 1 x2 1 9(cid:1) . Write the negation of r using logic symbols but do not use the symbol ": (1 mark) ( x r)(|x 1| 2 x z) (cid:0)(x2 1 < 1) (x2 1 > 9)(cid:1) For any real number c, the quadratic equation x2 + x + c4 = 0 has two distinct real solutions. R is false: let f ={0 , 1 , a} be a eld with three elements. Fill in the blanks with either 0, 1, or a. (2 marks) 1 + a 1 = 0 a + a = 1: given a = [ 1, 3) z and b = {x n : |x 1| < 2}.