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Method and examples
Mathematical Logic, truth tables, logical equivalence
 1. Prepare the truth table Logical Expression pvvqp^^q=q^^p(pvvq)vvr=pvv(qvvr)(p^^q)^^r=p^^(q^^r)~(pvvq)=~p^^~q~(p^^q)=~pvv~qp^^(qvvr)=(p^^q)vv(p^^r)pvv(q^^r)=(pvvq)^^(pvvr)p^^(pvvq)=ppvvt=tp^^c=cp=>q=q=>pp<=>q

 2. Examine the logical validity of the argument Hypothesis Conclusion Hypothesis : pvvq;~p and Conclusion : qHypothesis : (p^^~q)=>r;pvvq;q=>p and Conclusion : rHypothesis : p=>q;q=>r and Conclusion : p=>rHypothesis : p=>q;p and Conclusion : qHypothesis : p=>q;p=>r and Conclusion : p=>(q^^r)
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