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(Solved): Hello! Please help me. :(  Please make a truth table for each question and put if it is Valid o ...


Hello! Please help me. :(  
Please make a truth table for each question and put if it is Valid or Invalid and place an X next to the line that is Valid or Invalid 
Thank you! 

1) P & Q, Q & P  |-  P -> Q 
2) P -> Q, P -> R  |-  Q -> R 
3) P & ~Q, Q & ~R |-  R & ~P 
4) P <-> ~R, R <-> ~P |-  R <-> P 



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Solution Given that, 1) P & Q, Q & P |- P -> Q That is, P ? Q ( premise - 1) Q ? P ( premise - 2) ? ( P ? Q ) ( Conclusion ) Truth table P Q P ? Q Q ? P P ? Q T T T T T X T F F F F F T F F T F F F F T The truth table ( 2nd row ) shows that, the true
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