Check that the following arguments are valid without using a truth table

1.
(F&G)v(H&-I)
I-> -(F&D)
_________
I-> -D

2.
G-> (H&-K)
H <-> (L&I)
-IvK
-----------
-G

3.
F->(-GvH)
F->G
-(HvI)
------------
F->J

4.
FvH
-H<->(LvG)
(G&B)v[G&(K->G)]
-----------
F

5.
(-HvJ)vK
K-> -I
-------
(H&I)->J

6.
(Av-B)v-C
(DvG)vC
--------------
-A -> [B->(GvD)]

7.
G&(A&N)
(A<-> -M)&(N->M)
----------
F

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