Complete each proof using only the eight Inference Rules.

1. [ solution ]

1. d&e
2. g&h
3. gve
4. (g&e)->j    /.:j

 

 

2. [ solution ]

1. p&~q
2. (~r->t)vq
3. p->(s->~r)    .:s->t

 

 

3. [ solution ]

1. h->i
2. (e->g)&(gvj)
3. (ive)&(hve)
4. (gv~k)&(iv~l)    /.:ivg

 

 

4. [ solution ]

1. (~k&~q)->{(~r->~b)&(~s->k)}
2. ~sv~r
3. k->q
4. i&~q /.:~b

 

 

 

 

5. [ solution ]

1. (pvr)&~p
2. (rvc)->(p->k)
3. (~pvd)->(r->l)    /.:kvl

 

6. [ solution ]

 

1. {(m&n)vo}->r
2. o&m
3. o->n
4. ovs   /.:rvs