Question

In this assignment you will write code that will prove both equations for three logical equivalences (pick any three except the double negative law). Below is the list of logical equivalences. Please create a program that allows a user to test logical equivalences and have proof of their equivalency for the user. The rubric is below. Submit screen shots of the code, input, and output of the program. Theorem 2.1.1 Logical Equivalences Given any statement variables p, q, and r, a tautology t and a contradiction c, the following logical equivalences hold. 1. Commutative laws: P N 454P PVq=9VP 2. Associative laws: ( pq) Ar=p1qar) (pvq) vr=pv (vr) 3. Distributive laws: p(qvr) =( pq) v ( pr) pv (qar) = (pv q) (p vr) 4. Identity laws: pat=p pvc=p 5. Negation laws: PVp=t PA-p=c 6. Double negative law: (p) =p 7. Idempotent laws: pap=p рурар 8. Universal bound laws: pvtat pic=c 9. De Morgan's laws: (p. 9) = -PV-9 -(PVq) = -19 10. Absorption laws: pv ( pq) =p PA (pv q) =p 11. Negations of t and c:

Answer 1

=my_script.m RUN Vars [1x4] - out 1 2 3 [1x4] [1x4] 11 12 %commulative law %commulative law function test=my_script p=input("enter values of p: "); q=input("enter values of g: "); %function to find allp function output1=commulativel(p, q) output1=q1p; end %function to find q&p function output2=commulative2(P,9) output2=9&p; end % first finding plla x=pla % first finding p&q y=p&q output1=commulativel(p,q) output2=commulative2(,9) if(x==output1 && y=-output2) display("commulative law is proved") end end 16 18 octave: 12> my_script([0 0 1 1], [O 1 0 1]) enter values of p: > [0 0 1 1] enter values of q: > [0 1 0 1] X = 0 1 1 1 y = 0001 output1 = 1 1 1 output2 = 0001 commulative law is proved

#ans 2 %DISTRIBUTIVE LAW %DISTRIBUTIVE LAW function test=my_script() p=input("enter values of p: "); q=input("enter values of q: "); r=input("enter values of r: "); %function to find (p&q)|(p&r) function output1=commulativel(p,q,r) output1=(p&q) (p&r); end %function to find (19)&(pr) function output2=commulative2(p,q,r) output2=(p19)&(pr); end % first finding p&(q|r) x=p&(ar) % first finding pl(q&r) y= pl(q&r) output1=commulativel(p,q,r) output2=commulative2(p,q,r) if(x==output1 && y=-output2) display("Distributive law is proved") end end 16 17 18 19 20 octave:4> my_script() enter values of p: > [000011 1 1] enter values of q: > [001100 1 1] enter values of r: > [0 10 10 10 1] X = 0 0 0 0 0 1 1 1 y = 0 0 0 1 1 1 1 1 output1 = 0 0 0 0 0 1 1 1 output2 = 0 0 0 1 1 1 1 1 Distributive law is proved

# ans 1 2 00 OU 10 %De Morgan's LAW %De Morgan's LAW function test=my_script() p=input("enter values of p: "); q=input("enter values of q: "); %function to find mpa function output1-commulative1(,9) output1=wp ~; end %function to find wp&nq function output 2-commulative2(p, q) output2=wp&mq; end % first finding ~(p&q) X=n(p&q) % first finding (pla) y=n(pl) output1=commulativel(p, q) output2=commulative2(P,9) if(x==output1 && y=-output2) display("De Morgan's law is proved") end end 13 14 15 16 17 18 octave:7> my_script() enter values of p: > [0 0 1 1] enter values of q: > [O 1 0 1] X = 1 1 1 0 y = 1 000 output1 = 1 1 1 0 output2 = 1 000 De Morgan's law is proved