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===Analysis of contingent propositions===
===Analysis of contingent propositions===
−{| align="center" cellpadding="8"
{| align="center" cellpadding="8"
| [[Image:Logical Graph (P (Q)) (P (R)).jpg|500px]] || (26)
| [[Image:Logical Graph (P (Q)) (P (R)).jpg|500px]] || (26)
|}
|}
−{| align="center" cellpadding="8" style="text-align:center"
{| align="center" cellpadding="8" style="text-align:center"
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| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q \texttt{))~(} p \texttt{~(} r \texttt{))}</math>
| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q \texttt{))~(} p \texttt{~(} r \texttt{))}</math>
|}
|}
−{| align="center" cellpadding="8" style="text-align:center"
{| align="center" cellpadding="8" style="text-align:center"
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| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q ~ r \texttt{))}</math>
| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q ~ r \texttt{))}</math>
|}
|}
−{| align="center" cellpadding="8"
{| align="center" cellpadding="8"
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−====Equation 1 : Proof 1====
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−====Equation 1 : Proof 2====
+=====Single Image Version=====
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−=====Serial Image Version=====
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| (31)
| (31)
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−{| align="center" cellpadding="8"
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−====Proof 3====
+====Equation 1 : Proof 3====
{|
{|
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=====Variant 2=====
=====Variant 2=====
+
+{| align="center" cellpadding="8"
+|
+{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-00.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-01.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cast P.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-02.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-03.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-04.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Emptiness.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-05.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-06.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cast Q.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-07.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-08.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-09.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-10.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Spike.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-11.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-12.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cast R.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-13.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-14.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Emptiness.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-15.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Spike.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-16.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
+|-
+| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-17.jpg|500px]]
+|-
+| [[Image:Equational Inference Bar -- QED.jpg|500px]]
+|}
+| (40)
+|}
+
+===Praeclarum Theorema : Proof by CAST===
{| align="center" cellpadding="8"
{| align="center" cellpadding="8"
