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Question

Examine whether the following statement pattern is tautology, contradiction or contingency: $$p \vee \sim (p \wedge q)$$


Solution

 $$p$$
$$q$$ 
 $$p\wedge q$$
 $$\sim \left( p\wedge q \right) $$
$$p\vee \sim \left( p\wedge q \right) $$ 
 T
 T 
 T 
  F

 T
 F
 F 
  T 

 F
 T
 F 
  T
T
 F
 F 
 F 
  T 

Therefore, the statement: $$p\vee \sim \left( p\wedge q \right) $$ is tautology.

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