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Written as a string, this is just the concatenation "<math>p~q</math>".

Written as a string, this is just the concatenation <math>p~q</math>.

The proposition <math>pq\!</math> may be taken as a boolean function <math>f(p, q)\!</math> having the abstract type <math>f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is read in such a way that <math>0\!</math> means <math>\operatorname{false}</math> and <math>1\!</math> means <math>\operatorname{true}.</math>

The proposition <math>pq\!</math> may be taken as a boolean function <math>f(p, q)\!</math> having the abstract type <math>f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}</math> is read in such a way that <math>0\!</math> means <math>\operatorname{false}</math> and <math>1\!</math> means <math>\operatorname{true}.</math>

This expression follows because the expression <math>p + \operatorname{d}p,</math> where the plus sign indicates addition in <math>\mathbb{B},</math> that is, addition modulo 2, and thus corresponds to the exclusive disjunction operation in logic, parses to a graph of the following form:

This expression follows because the expression <math>p + \operatorname{d}p,</math> where the plus sign indicates addition in <math>\mathbb{B},</math> that is, addition modulo 2, and thus corresponds to the exclusive disjunction operation in logic, parses to a graph of the following form:

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| [[Image:Cactus Graph (P,dP).jpg|500px]]

|                       @                        |

|                    (p, dp)                     |

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