Question

Discrete Math- Check my work and explain if I got anything wrong

7. Prove that the following formulas Fi and F2 are equivalent: F1:-(3x (p(x) (Fy (g(y) 1-r(x, y))))) F2: Vx (p(x) → (Vy (q(y) +r(x, y)))) Clearly label each equivalence used in your proof.

Answer 1

Your approach is absoluley Correct. {i} (15)*7(34 (ponafeyrary 179029) Rulep {v} %) va 7(0)30 (7) (919) 9740749Rules lawo negatrow'7 (3x) prax=) +nJpgy {io (Tres anyagfesa person law of negation 1 (za pen)A+265 pcy) {i} (4) en TRW ulay (721w seny) mungons law {r} (5) #a( 7pcoWy ( 919–1 (29)))) Rulet . Equivalent formula 7 9 (9) v Y(39)(s) 1 9)- (114) . i apva (7) P al { (6) + ( P(x)>(Vu C24)– YC3,90) Rule] the same equivalent formula A pvc by (a(4) _) 8 (2,4))) (=) P-) (by (942) (8.37) le f: to posy (7y (249) -861.9))) F is equivalent to F. F F F 2 1F, (=) F2 ) Rulep: Rules: given premises Implications & quivalence formulas