Quiz Instructions

Select ALL that apply!

Some questions may have multiple correct answers!

Question 1 5 pts Determine which of the following sentences are logical statements :] Welcome to USF 3 If 0>2 then the dolphin is a mammal j lam falling asleep right about now 3 Can I stop reading this? :] You better sit down. Question 2 5 pts The implication between two statements can be described as: _ negation of the conjunction of the two statements M negation of the rst statement OR the second statement j negation of the conjunction between the rst statement and negation of the second statement 3 negation of itself :] none of the above Question 3 5 pts Determine which of the following statements are true 3 "A B" if and only if 1 + 2 = 2' 3 If 1 + 1 = 2 then black is white. 3 (2-3>1 or 3'4 y > z . O X > Z . O none of the above D Question 5 5 pts Suppose p and q are these propositions: p : "I go swimming' q : "it is a hot day." Express in symbols the compound proposition "I don't go swimming but it is a hot day." O - paq O - pv q O - PA - q O - pv - q O none of the aboveQuestion 6 5 pts The implication e q > p is true for all possible assignments of truth values for p and 11 except for which assignment? 0 p false, 4 false. 0 p true. q true 0 p true. q false. 0 p false, 4 true. 0 none of the above Question 7 5 pts The biconditional p e q is False for all possible assignments of truth values forp and q except for which assignment(s)? p true, q false, p false, q true, p false, 4 false. C C l: p true, q (me C C none of the above Question 8 5 pts Which implication is logically equivalent to the implication r > es ? Os>~r' OHS)I't Ows>~r. Oar>es. 0 none of the above D Question 9 5 pts Let p be "Jane works late", let q be "Amy works late", and let r be "they will eat at the restaurant". Consider the proposition "If Jane or Amy do not work late, then they will eat at home." Which of these represents the proposition in symbols? O -(pvq) - -r. 1 -p) O ( p - q) v (s-> t) O (paris) v ( -s A -p ) v -s O none of the aboveU Question 11 5 pts Lets consider the following two statements: A = (p v~ql A r B=[(pAq)->(pvq)l->~q Which of the following is True: :] The truth table for statement A has more rows than the truth table for statement B :] The truth table for statement A has less rows than the truth table for statement B :] The truth tables for both statements have same number of rows 3 The truth table for statement A has more columns than the truth table for statement B j The truth table for statement A has less columns than the truth table for statement B j The truth tables for both statements have same number of columns U Question 12 5 pts Construct a truth table for [(P>q) v wp] A eq and answers the following questions: 1, How many rows will the table have? 2, How many columns will the table have? 3, What are the truth values in the last column? Please write in the following format: TFTFFTF, one value for each row for thelast column, D Question 13 5 pts Construct a truth table for [(p->q) A -p] v r and give the answers to the following questions: 1. How many rows will the table have? 2. How many columns will the table have? 3. What are the truth values in the last column? Please write in the following format: TFTFFTF, one value for each row for thelast column. D Question 14 5 pts Let's consider the following statement: (p ^ -q) v (r ^ -q) Select the statement that is derived from the given statement applying only the distributive law. note: apply the distributive law from right to left Op ( - q vr ) O - q v (par ) Or (-qvp ) O - qa (p vr ) O - q v (pvr) O none of the aboveD Question 15 5 pts Let's consider the following logical statement: [(p v T) -> (F , q)] v (p , -p) v (q v -q). Which of the following statement are logically equivalent to the given statement: OT OF O q Op Opvq O none of the above D Question 16 5 pts Let's consider the following logical statement: [(p v T) - (T , q)] v (p A -p) v (pv F). Which of the following statement are logically equivalent to the given statement: O T OF O q Op Op vq none of the aboveU Question 17 5 pts Show, using truth table, that (p /\\ q) ) (p v q) is a tautology' Please follow the assignment of truth values for p and q as we have done in class (p: TTFF, q: TFTF) [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V [Select] V D Question 18 5 pts Show, without using truth table, that (p / q) - (p v q) is a tautology. note: please type up the answer in the box bellow. You can do so either by using the Insert Equation tool and type up each symbol ( A, V, -, =), or just by copying and pasting those symbols (from anywhere you want) in the box where you need them. Just make sure they show properly. Any way you decide to write up the answer, make sure you show each line as you modify the statement using the logic laws, do not skip steps. Edit View Insert Format Tools Table 12pt " Paragraph B I U A v & v TV y v EV EVE TO BV VX CO p ERS9 1 0 words >Question 19 5 pts Check if (q > p) > s and (q v s) A (-vp v s) are logically equivalent by constructing a single truth table. After you have constructed the truth table, answer the following questions: 1. How many rows will the table have? 2' How many columns will the table have? 3' Are the two statements logically equivalent? (answerY or N). D Question 20 5 pts Show, without using truth table, that (q -> p) -> s and (q v s) A (-p v s) are logically equivalent. note: please type up the answer in the box bellow. You can do so either by using the Insert Equation tool and type up each symbol ( A, V, -, =), or just by copying and pasting those symbols (from anywhere you want) in the box where you need them. Just make sure they show properly. Any way you decide to write up the answer, make sure you show each line as you modify the statement using the logic laws, do not skip steps. Edit View Insert Format Tools Table 12pt Paragraph BIUA QV T V y v v EVE To VX p O words >