Name (printed):Student ID #:Section # (or TA’s:name and time)CMSC 250 Quiz #2 ANSWERS Wednesday, Feb. 4, 2004Write all answers legibly in the space provided. The number of points p os sible 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.1. [15 points] Create a complete truth table to determine if the following statement is a tautology. Use1 for “true” and 0 for “false” to complete the truth table (rather than T and F).• ∼ ((p ∧ q) ∧ r) ∨ (p∧ ∼ (r ∨ q))a b c dp q r p ∧ q (p ∧ q) ∧ r ∼ a r ∨ q ∼ (r ∨ q) p ∧ c b ∨ d1 1 1 1 1 0 1 0 0 01 1 0 1 0 1 1 0 0 11 0 1 0 0 1 1 0 0 11 0 0 0 0 1 0 1 1 10 1 1 0 0 1 1 0 0 10 1 0 0 0 1 1 0 0 10 0 1 0 0 1 1 0 0 10 0 0 0 0 1 0 1 0 12. [3 points] Your truth table s hows it to be a tautology (circle one)? (NO)3. [3 points]Indicate the location or locations in the truth table that led you to this c onclusion andexplain (in one sentence) why you reached this conclusion.The first line has a 0 (false value). It can onlybe a tautology if all of the lines have 1 (true value).↓ TURN OVER ↓4. [6 points] Given the following statements. Give the representation for each of the given compoundstatements using only the statement symbols and the ∧(and), ∨(or)and ∼ (not) symbols. And thestatements refer to some moment in time (that over time people can change their minds on who theylike).• A = Alice likes Fred.• B = Bob likes Fred.• C = Carol does not like Fred.a. Alice, Bob and Carol like Fred. (A ∧ B)∧ ∼ Cb. Alice and Bob don’t like Fred, and Carol does like Fred. ∼ A∧ ∼ B∧ ∼ Cc. Alice likes Fred and exactly one of the other two also like Fred. A ∧ ((B ∧ C) ∨ (∼B∧ ∼ C))5. [3 points] Give the alias under which you would like your grades posted. If you do not want yourgrades posted, give the alias “NONE”. If you give an alias, it will only be known to the instructors,TAs and yourself. This way you will be able to keep track of your grades and how you compare toother students without revealing which student has which grades.any name here as long as it is
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