CHAPTER 0 TEST*No calculators, no cell phones, just you and a pen/pencil/Math 231September 3, 2008 Name:By printing my name I swear by the honor code.1. Determine whether each of the following statements is true (T) or false (F).T F If a is a real number, then −a is negative.T F If x > 2, then x ≥ 3.T F There exists an integer x such that x ≤ 1 and x ≥ 2.T F 3.5 ∈ {x ∈ R | x − 4 > 0}.2. Complete each of the following theorems. In each case A and B are real numbers orexpressions.AB = 0 if and only if:AB= 0 if and only if:AB > 0 if and only if:3. For the statement “If |x| ≤ x, then x is positive,” write down...the converse:the contrapositive:the negation:a counterexample:4. Circle the inequality on the left whose solution s et is shown on the right.A) |x − 3| < 2B) |x − 1| < 4C) |x − 1| < 5D) |x − 5| < 11 55. State the quadratic formula theorem and explain how to prove it. Don’t actually proveit or do any of the algebra steps, but carefully and clearly explain what would have tobe done to prove it.6. Solve the inequality4x − 1≥ 2using the method of “cases” that was done in class and in the reading. Show all workclearly and in order. Take your time and write it up neatly, please. The quality ofyou r work and reasoning is worth more than your final