Name (printed):Student ID #:Section # (or TA’s:name and time)CMSC 250 Quiz ANSWERS #2 Wednesday, Sept. 7, 2005Write all answers legibly in the space provided. The number of points possible for each question is indicatedin square brackets – the total number of points on the quiz is 30, and you will have exactly 15 minutes tocomplete this quiz. You ma y not use calculators, textbooks or any other aids during this quiz.1. [10 pnts.]Determine if the following three statemen ts are logically equivalent by using a SINGLE,COMPLETE truth table. Use 1 for “true” and 0 for “false” to complete the truth table.a. (p ∧ r) ∨ rb. (p ∨ r) ∧ (∼ p ∨ r)c. rp r ∼ p p ∧ r (p ∧ r) ∨ r p ∨ r ∼ p ∨ r (p ∨ r) ∧ (∼ p ∨ r)1 1 0 1 1 1 1 11 0 0 0 0 1 0 00 1 1 0 1 1 1 10 0 1 0 0 0 1 0YES (Yes or No) These statemen ts are logically equivalent.2. [6 pnts.]Give one possible value for the integer n in eac h of the following which would make thestatement true. (If there is no possible value, write the word “impossible”.)• p=(n ≤ 1)• q=(n =3)• r=(n ≥ 7)a. ∼ (p∨∼q){2, 4, 5, ...}b. (p ∧ r) ∧ q impossible↓ TURN OVER ↓3. [14 pnts.] Give the complete truth table of the following statement. Then answer the question posedbelow based on your results.(∼ (a∨∼b) ∧ (a∨∼c)) ∧ (b ∧ a)x y w za b c ∼ b ∼ c a∨∼b ∼ (a∨∼b) a∨∼c x ∧ y b ∧ a w ∧ z1 1 1 0 0 1 0 1 0 1 01 1 0 0 1 1 0 1 0 1 01 0 1 1 0 1 0 1 0 0 01 0 0 1 1 1 0 1 0 0 00 1 1 0 0 0 1 0 0 0 00 1 0 0 1 0 1 1 1 0 00 0 1 1 0 1 0 0 0 0 00 0 0 1 1 1 0 1 0 0 0Give values for each of the following variables to describe one situation where this statement wouldbe true. Indicate the value of that variable by circling either the true or the false on that line.ANSWER : NONEa TRUE FALSEb TRUE FALSEc TRUE FALSE4. Give an alias - a madeup name you will associate with yourself - under which you would like yourgrades posted. If you do not want to have your grades posted, specify the alias
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