Logic
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High School Geometry
High School Geometry
Math

 Name _____________________________ Date ___________________
Logic
Determine which of the following statements are a tautology or a contraction.

 1 ~ q ~ q
 2 p ( p p )
 3 ~(~ p p )
 4 p ( p ~ p )
 5 q ~ q
 6 ~ q ~(~ q q )
 7 (~ q q )(([~(~ q ~ q )]) q )
 8 ([~( p q )]) p
 9 (( p p )(~ p p ))(~(~ p p ))
 10 ((~ p ~ q )~( p ~ q ))(~( p q ))
 11 ~(~ p q )
 12 (( q ~ p )(~ p ~ q ))(~( p (~ q p )))
 13 ( p ~ p )(~(~ p p ))
 14 (~( p p ))(( p p )( p p ))
 15 ~(~ p q )(~ q ~ p )
 16 ~(( p (~ p p ))(~(~ p p )))
 17 (~(( p ~ p )(~ p p )))(~ p ~ p )
 18 (~( p ~ q ))( p ( p q ))
 19 p q
 20 (~ p ~ q )(([~(~ p ~ q )]) p )
 21 (( q p )( q p ))(( q ~ p ) q )
 22 (~(~ q q ))( q ~ q )
 23 ( p ~ q )(~ p q )
 24 ~(( p ~ p ) p )
 25 (~ p ~ p )( p p )
 26 (~( p (~ q p )))(~ p ~ q )

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Logic
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