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Watson-Crick Base Pairing

Adenine pairs with Thymine, and Guanine pairs with Cytosine, forming the fundamental structure of DNA and RNA.
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The statement of the theorem

Let B={A,T,G,C}B = \{A, T, G, C\} be the set of nucleobases. Define the pairing function P:B×B→{0,1}\mathcal{P}: B \times B \to \{0, 1\} such that P(b1,b2)=1\mathcal{P}(b_1, b_2) = 1 if b1b_1 and b2b_2 form a canonical pair, and P(b1,b2)=0\mathcal{P}(b_1, b_2) = 0 otherwise. The canonical pairing rules are defined by the constraints:\nP(A,T)=1,P(T,A)=1,P(G,C)=1,P(C,G)=1\mathcal{P}(A, T) = 1, \quad \mathcal{P}(T, A) = 1, \quad \mathcal{P}(G, C) = 1, \quad \mathcal{P}(C, G) = 1 \nAnd for all other pairs (b1,b2)∉{(A,T),(T,A),(G,C),(C,G)}(b_1, b_2) \notin \{(A, T), (T, A), (G, C), (C, G)\}, P(b1,b2)=0\mathcal{P}(b_1, b_2) = 0. This pairing dictates the formation of a stable base pair P=(b1,b2)P = (b_1, b_2).