Truth tables for single statements

For each statement do a truth table, and determine whether the statement is a tautology, contingency or contradition.

 

 

1.p&~p
[ solution ]

 

2.(pv~p)->(p&~p)
[ solution ]

 

3.{(x&~y)->x}->y
[ solution ]

 

4.~av{(avb)v~a}
[ solution ]

 

5.{(p<->q)&~p}<->~p
[ solution ]

 

6.{~(d&~e)vg}&~g
[ solution ]

 

7.(jv~k)&{~k->(~l&l)}
[ solution ]

 

8.[~cv{(~r<->r)v(s&~s)}]<->~c
[ solution ]

 

9.{wv(~y&r)}->{xv(~xvw)}
[ solution ]

 

10.(p&~p)->(r&~s)
[ solution ]

 

11.(p<->q)<->{(p&q)v(~p&~q)}
[ solution ]