# Thread: Proving if Equivalent without proof tables

1. ## Proving if Equivalent without proof tables

Heyy i would really appriciate some hints or help for this question ( Attachment)

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

2. Originally Posted by kensington
Heyy i would really appriciate some hints or help for this question ( Attachment)

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
$P\Rightarrow Q\equiv \sim P\lor Q$

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