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Home > College Algebra calculators > Mathematical Logic, truth tables, logical equivalence example
Mathematical Logic, truth tables, logical equivalence example ( Enter your problem )
( Enter your problem )
  1. Laws of logical connectives
  2. Prove Commutative laws
  3. Prove Associative laws
  4. Prove De-Morgan's laws
  5. Prove Distributive laws
  6. Prove Negation law
  7. Prove Absorption laws
  8. Laws for Tautology
  9. Laws for Contradiction
  10. Implication
  11. Double Implication
 		Other related methods
  1. Definitions
  2. Laws of logical connectives
  3. Prepare the truth table
  4. logical validity of the argument
5. Prove Distributive laws
(Previous example)		7. Prove Absorption laws
(Next example)

6. Prove Negation law


Prove Negation law

1. not(not p) = p

Solution:
To prove `~(~p)=p`, we have to first prepare the following truth table


`(1)``(2)=~(1)``(3)=~(2)`
`p``~p``~(~p)`
TFT
FTF


from this table, we can say that columns (3) and (1) are identical.
`:. ~(~p)=p`




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5. Prove Distributive laws
(Previous example)		7. Prove Absorption laws
(Next example)


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