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

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Logic
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Number of Keys
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Number of Pages (for each key)
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