4. Please note that the submitted work must represent your own thinking and effort. Copying the work of others will nor be tolerated. 5. Please submit within the due time (see above). Late submissions are not accepted. Answer the following: 1) What is the negation of this proposition? [0.5pt] "Either a0 or a is a positive integer" a) a0 or a is not a positive integer b) a0. [I/F] 12) Determine whether this biconditional is true or false. [0.5pt] 5+1=6 if and only if the sky is green. [T/F] 13) Determine whether this biconditional is true or false. [0.5pt] 4+3=6 if and only if there are 70 minutes in one hour. [T/F] 14) Find the output of the following combinatorial circuits (show intermediate values to the right of each gate). [2 pts] a) (pq)(pq) b) (pq)(pq) c) (pq)(pq) d) None of them b) c) d) None of thern 16) Use De Morgan's laws to find the negation of the statement. "The stukent will have a class tomorrow or will have ar exam. " [1pt] a) The student will have a class tomorrow and will have an ecam. b) The student will have a class tomorrow and will not have an exam. 6). The student will hot have a class tomorrow asd will bot hrve an cxam. d) The student will not have a class tomorrow or will bot have an exam. (8) t sing truth-tables, check the veracity of the followi-g statemint: {0.5, Fy] - ((i+1)(s1))(tr)) is cquivalent to (t(At)) 19) Using truth-tables, check the veracity of the following statement [0.5 t.s ] ((rt)(st))(tt)) is not equivalent to ((rt)(1t))(tt)) [T /F] 20) Using tnath-tables, chock the veracity of the following statement {0.5pts}: ((rt)(sAt))A(tr)) is equivalent to ((rt)(sAt))A(tr)) [T/F) [T/H] [T/F] [T/F] 21) Answer the following question by selection the appropriare supporting evidence for each logical equivalence: [0.5pt] (rs)(qr)=(qr)(rs) a) De Morgan "s Law b) Commutative Law c) Distributive Law d) Absorption Law 22) Answer the following question by selection the appropriate supporting evidence for each logical equivalence: {0.5pt] (rs)(qr)=(rs)(qr) a) De Morgan's Law b) Commutative Law c) Domination Law d) Associative Law 23) Answer the following question by selection the appropriate supporting evideace for each logical equivalence: [0.5pt] (rs)((rs)p)(rs) a) De Morgan's I aw b) Commutative Law c) Domination Law d) Absorption Law A) Answer the following question by sclection the appropriate supporting evidence for each logical equivalence: [0.5pr} ((rs)(qr))T(rs)A(qr) a) De Morgan's Law b) Idempotent Law 2 opertine the truth value of the folloning atatement if the domiain of tack variable consias of all [T]F] pat permiae the truich value of the following statemitht if the domain of each variable centists of alf. inesen ? x2. 47) peeermine the truth value of the following statement if the domain of each variable cotsists of all Vx: x2+2