Demostrar x<6
(1)x>y V x<6
(2)x>y → x>4
(3)x>4 → x=5 & x<7
(4)x<6 → x=5 & x<7
(5)x<7 & x=5 → z>x V y<z
(6)x>y → ~(y<z V z>x)
(7)x>y → x=5 & x<7 HS 2-3
(8)(x=5 & x<7) V (x=5 & x<7) DS 1-4-7
(9) x=5 & x<7 DP 8
(10) x<7 & x=5 CL 9
(11) z>x V y<z MPP 5-10
(12) y<z V z>x CL 11
(13) ~(x>y) MTT 6-12
(14) x<6 MTP 1-13
Demostrar ~(A V B)
(1)C & ~D
(2)C → ~A
(3)D V ~B
(4)C Sim 1
(5)~A MPP 2-4
(6)~D Sim 1
(7)~B MTP 3-6
(8)~A & ~B AD 5-7
(9)~( A V B) DL 8
Demostrar x<y & y=6
(1)x<y ↔ y>4
(2)Y=6 ↔ x+y=10
(3)y>4 & ~( x+y ≠ 10)
(4)y>4 → x<y LB 1
(5)y>4 Sim 3
(6)x<y MPP 4-5
(7)x+y=10 → Y=6 LB 2
(8)~( x+y ≠ 10) Sim 3
(9)X+y=10 DN 8
(10) Y=6 MPP 7-9
(11) x<y & Y=6 Ad. 6-10
