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Mathematical Logic, truth tables, logical equivalence example ( 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

1. Definitions
(Previous method)
2. Prove Commutative laws
(Next example)

1. Laws of logical connectives





1. Commutative laws
1. `p vv q = q vv p`
2. `p ^^ q = q ^^ p`

2. Associative laws
1. `(p vv q) vv r = p vv (q vv r)`
2. `(p ^^ q) ^^ r = p ^^ (q ^^ r)`

3. De-Morgan's laws
1. `~(p vv q) = ~ p ^^ ~ q`
2. `~(p ^^ q) = ~ p vv ~ q`

4. Distributive laws
1. `p ^^ (q vv r) = (p ^^ q) vv (p ^^ r)`
2. `p vv (q ^^ r) = (p vv q) ^^ (p vv r)`

5. Negation law
1. `~(~ p) = p`

6. Absorption laws
1. `p ^^ (p vv q) = p`
2. `p vv (p ^^ q) = p`



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1. Definitions
(Previous method)
2. Prove Commutative laws
(Next example)





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