Logic Worksheet 15     Circle the valid arguments, and cross out the invalid ones.

1. ~(Cl ^ Bk)		2. ~(Cl ^ Bk)	  	3. ~(Cl ^ Bk)	  	4. ~(Cl ^ Bk)	
    ~Cl v ~Bk		    ~(Cl v Bk)		    ~Cl ^ ~Bk		    ~Cl ^ Bk	

5. ~(Cl ^ Bk)	  	6. ~(Cl v Bk)		7. ~(Cl v Bk)	  	8. ~(Cl v Bk)	
   ~Cl v Bk 		    ~Cl ^ ~Bk		    ~(Cl ^ Bk)		    ~Cl v ~Bk

9. ~(Cl v Bk)	  	10. ~(Cl v Bk)	  	11. ~Cl v ~Bk		12. ~Cl v ~Bk
 ~Cl v Bk		      ~Cl ^ Bk 		      ~(Cl ^ Bk)		      ~Cl ^ Bk

13.  ~Cl v ~Bk		14. ~Cl v ~Bk		15. ~Cl v ~Bk		16. ~Cl ^ ~Bk
       ~(Cl ^ ~Bk)	      ~Cl ^ ~Bk		      ~(Cl v Bk)		      ~(Cl v Bk)

17. ~Cl ^ ~Bk	 	18. ~Cl ^ ~Bk	 	19. ~Cl ^ ~Bk	 	20. ~Cl ^ ~Bk
      ~(Cl ^ Bk)		       ~Cl v ~Bk		       ~Cl v Bk		        ~Cl ^ Bk
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Now circle pairs of arguments in which both arguments are valid.

1. ~(Cl ^ Bk)		~Cl v ~Bk
    ~Cl v ~Bk		~(Cl ^ Bk)

2. ~(Cl ^ Bk)		~(Cl v Bk)	
 ~(Cl v Bk)		~(Cl ^ Bk)

3. ~(Cl ^ Bk)		~Cl ^ ~Bk
 ~Cl ^ ~Bk		~(Cl ^ Bk)

4. ~(Cl ^ Bk)		~Cl ^ Bk
  ~Cl ^ Bk		~(Cl ^ Bk)

5. ~(Cl ^ Bk)		~Cl v Bk
 ~Cl v Bk		~(Cl ^ Bk)

6. ~(Cl v Bk)		~Cl ^ ~Bk
 ~Cl ^ ~Bk		~(Cl v Bk)

7. ~Cl ^ ~Bk		~Cl ^ Bk
    ~Cl ^ Bk 		~Cl ^ ~Bk
8. ~(Cl v Bk)		~Cl v ~Bk
    ~Cl v ~Bk		~(Cl v Bk)

9. ~(Cl v Bk)		~Cl v Bk	
    ~Cl v Bk		~(Cl v Bk)

10. ~(Cl v Bk)		~Cl ^ Bk
      ~Cl ^ Bk		~(Cl v Bk)

11. ~Cl ^ ~Bk		~Cl v Bk
    ~Cl v Bk		~Cl ^ ~Bk

12. ~Cl v ~Bk		~Cl ^ Bk
   ~Cl ^ Bk		~Cl v ~Bk

13.  ~Cl v ~Bk		~(Cl ^ ~Bk)
    ~(Cl ^ ~Bk)	~Cl v ~Bk

14. ~Cl v ~Bk		~Cl ^ ~Bk
   ~Cl ^ ~Bk		~Cl v ~Bk
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Finally, and to practice for the inevitable quiz, go through the first set of arguments again, this time ignoring the issue of validity, pick out all and only the arguments that represent instances of de Morgan's laws, and draw squares around those arguments.