Logic
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   High School Geometry
High School Geometry
Math

 

(pre-made sample)
Name _____________________________
Date ___________________
Logic
Determine which of the following statements are a tautology or a contraction.


1.   ~ q q

2.   (~ p ~ p )( p ~ p )

3.   ~(~ q ~ q )

4.   p ~ p

5.   ~(~ q ~ q )

6.   ( q q )(~ q ~ q )

7.   ~( p p )( p ~ p )

8.   (( p ~ q ) p )(~ p q )

9.   (~(~ q ~ q ))(~ q q )

10.   ~((~( p ~ p )(~ p p ))(( p p )(~ p p )))

11.   ( q ( p q ))( p (~ q p ))

12.   ( q q )(~ q q )

13.   ~((~( p p ))(~(~( p ~ p )~( p p ))))

14.   ~ p ~ q

15.   ( q ( q ~ q ))( q q )

16.   ( p (~ p p ))(~(( p ~ p )( p ~ p )))

17.   (~( p ( p ~ p )))(( p p )(~ p p ))

18.   ~( q ~ q )

19.   ~((~ p p )(~ p p ))

20.   ( q q )(~(~( q ~ q )~( q q )))

21.   (~((~ q p )(~ p ~ q )))(( p q ) q )

22.   (~ p ~ q )(~((~ q ~ p )( q p )))

23.   ~ p q

24.   ~((( q ~ q )( q q ))( q ~ q ))

25.   (~(~( q ~ q )~( q q )))(~ q q )

26.   (~ q q )(( q q )(~ q q ))


 


Answer Key


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   High School Geometry
High School Geometry
Math