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Method and examples
Mathematical Logic, truth tables, logical equivalence
1. Prepare the truth table
Logical Expression
  
  1. `pvvq`
  2. `p^^q=q^^p`
  3. `(pvvq)vvr=pvv(qvvr)`
  4. `(p^^q)^^r=p^^(q^^r)`
  5. `~(pvvq)=~p^^~q`
  6. `~(p^^q)=~pvv~q`
  7. `p^^(qvvr)=(p^^q)vv(p^^r)`
  8. `pvv(q^^r)=(pvvq)^^(pvvr)`
  9. `p^^(pvvq)=p`
  10. `pvvt=t`
  11. `p^^c=c`
  12. `p=>q=q=>p`
  13. `p<=>q`

2. Examine the logical validity of the argument
Hypothesis
Conclusion
  
  1. Hypothesis : `pvvq;~p` and Conclusion : `q`
  2. Hypothesis : `(p^^~q)=>r;pvvq;q=>p` and Conclusion : `r`
  3. Hypothesis : `p=>q;q=>r` and Conclusion : `p=>r`
  4. Hypothesis : `p=>q;p` and Conclusion : `q`
  5. Hypothesis : `p=>q;p=>r` and Conclusion : `p=>(q^^r)`
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