"555555-555 5.5555/5 Determine which of the following sentences are logical statements Welcome to USF If 0>2 then the dolphin is a mammal lam falling asleep right about now Can I stop reading this? You better sit down. "515555-552 W The implication between two statements can be described as: negation of the conjunction of the two statements negation of the rst statement OR the second statement negation of the conjunction between the rst statement and negation of the second statement negation of itself none of the above Wauesons esp/s Determine which of the following statements are true "A":"B" if and only if 1 + 2 = 2. If 1 + 1 = 2 then black is white. (2-3>1 or 3'4 p is true for all possible assignments of truth values for p and q except for which assignment? p false, q false. p true. q true. p true. q false. p false, q true. none of the above mouesony esp/s The biconditional p - q is False for all possible assignments of truth values for p and q except for which assignment(s)? p true. (1 false. p false, 4 true. p true. a true. p false, q false. none of the above Incorrect Question 8 0 / 5 pts Which implication is logically equivalent to the implication r- -s ? O star. O - s - r. O - star. O -r - - s. none of the above Incorrect Question 9 0 / 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? -(pvq) - - r. O ( - p 1 -q ) - -r. 0 - ( p xq ) -7 -r. O p -> ( - q 1 -r ) . O ( -p v - q) -> ar none of the aboveIncorrect Question 10 0 / 5 pts Eight is the number of rows in the truth table of which of the following statements: O ( - q q ) v (-q - 9 ) O (p -> -s) ~ (pv-s ) O (p v - q) ~ (r -> -p) O (p -> q) v (s-> t) (parAs) v (-SA -p) v-s none of the above Incorrect Question 11 0 / 5 pts Lets consider the following two statements: A = (pv-q) A-r B = [(p ~ q) - (pv q)] - -q Which of the following is True: O The truth table for statement A has more rows than the truth table for statement B O 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 O The truth table for statement A has more columns than the truth table for statement B O The truth table for statement A has less columns than the truth table for statement B O The truth tables for both statements have same number of columnsIncorrect Question 12 0 / 5 pts Construct a truth table for [(p->q) v -p] ^ -q and answers the following questions: 1. How many rows will the table have? 8 2. How many columns will the table have? 4 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. |TTTTFFTT Answer 1: 8 Answer 2: 4 Answer 3: TTTTFFTTmolest-on 13 W Construct a truth table for [(p>q) /\ ~p] v r and give the answers to the following questions: 1. How many rows will the table have? 8 2. How many columns will the table have? 4 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. F Answer 1: 8 Answer 2: 4 Answer 3: TTT F Incorrect Question 14 0 / 5 pts Let's consider the following statement: (p ^ -q) v (r A -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 Opa ( - q vr ) O - q v (par) OrA (- qvp ) O - qa (pvr ) O -qv(pvr) O none of the above Incorrect Question 15 0 / 5 pts Let's consider the following logical statement: [(p v T) - (F , q)] v (p A -p) v (q v -q). Which of the following statement are logically equivalent to the given statement: OT OF q Op Opvq none of the aboveIncorrect 0 / 5 pts Question 16 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: OT OF O a Op Opvq none of the aboveQuestion 18 Not yet graded / 5 pts Show, without using truth table, that (p A q) > (p v a) 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. Your Answer: @A@=:@V @AV@V "memo" 19 W, Check if (q a p) a s and (q v s) A (13 v s) are logically equivalent by constructing a single tmth table, After you have constructed the truth table, answer the following questions: 1. How many rows will the table have? 16 2. How many columns will the table have? 6 3. Are the two statements logically equivalent? (answerY or N). Y Answer 1: 16 Answer 2: Answer 3: Question 20 Not yet graded / 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. Your Answer: (q = p) =s : (9 p) VS -( -q V p) Vs (q A - p) Vs (q v s) = ( -PV s): - (q V s) V ( -p V s) (-9 1 - 8) V ( -q Vs) (-q v -p) A (-qVs) (-p V - q) (s V -q) (q A -p) Vs = (-pv-q) / (s V-q)