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Math Help - Proving if Equivalent without proof tables

  1. #1
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    Proving if Equivalent without proof tables

    Heyy i would really appriciate some hints or help for this question ( Attachment)
    Proving if Equivalent without proof tables-proof.jpg

    Do I have the right idea for this, please let me know

    (PvQ) ==> R (is the same as saying) ~R ==> ~P ^ ~Q (De Morgan's Theorem)

    (P==>R)^(Q==R) (is the same as saying (~R==>~P)^(~R==>~Q)

    ~R ==>~P ^ ~Q is the same as saying (~R==>~P)^(~R==>~Q)


    Any help is much appreciated
    Or would i make a proof table and say " refering to the proof table.."?

    Thanks
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  2. #2
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    Quote Originally Posted by kensington View Post
    Heyy i would really appriciate some hints or help for this question ( Attachment)
    Click image for larger version. 

Name:	proof.JPG 
Views:	12 
Size:	23.9 KB 
ID:	20703

    Do I have the right idea for this, please let me know

    (PvQ) ==> R (is the same as saying) ~R ==> ~P ^ ~Q (De Morgan's Theorem)

    (P==>R)^(Q==R) (is the same as saying (~R==>~P)^(~R==>~Q)

    ~R ==>~P ^ ~Q is the same as saying (~R==>~P)^(~R==>~Q)


    Any help is much appreciated
    Or would i make a proof table and say " refering to the proof table.."?

    Thanks
    P\Rightarrow Q\equiv \sim P\lor Q

    (P\lor Q)\Rightarrow R\equiv \sim(P\lor Q)\lor R\equiv (\sim P\land\sim Q)\lor R\equiv (\sim P\lor R)\land (\sim Q\lor R)\equiv (P\Rightarrow R)\land (Q\Rightarrow R)
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