Changes

The ''product'' of <math>x\!</math> and <math>y,\!</math> for values <math>x, y \in \underline\mathbb{B},</math> is given by Table&nbsp;8.  Viewed as a function of logical values, <math>\underline\cdot : \underline\mathbb{B} \times \underline\mathbb{B} \to \underline\mathbb{B},</math> this corresponds to the logical operation that is commonly called ''conjunction'' and otherwise expressed as <math>^{\backprime\backprime} x ~\operatorname{and}~ y ^{\prime\prime}.</math>  In accord with common practice, the raised dot <math>^{\backprime\backprime} \underline\cdot ^{\prime\prime},</math> underlined or not, is often omitted from written expressions.

The ''product'' of <math>x\!</math> and <math>y,\!</math> for values <math>x, y \in \underline\mathbb{B},</math> is given by Table&nbsp;8.  Viewed as a function of logical values, <math>\underline\cdot : \underline\mathbb{B} \times \underline\mathbb{B} \to \underline\mathbb{B},</math> this corresponds to the logical operation that is commonly called ''conjunction'' and otherwise expressed as <math>^{\backprime\backprime} x ~\operatorname{and}~ y ^{\prime\prime}.</math>  In accord with common practice, the raised dot <math>^{\backprime\backprime} \underline\cdot ^{\prime\prime},</math> underlined or not, is often omitted from written expressions.

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The "sum" of x and y, for values x, y ? B, is presented in Table 9.  Viewed as a function of logical values, + : B?B �> B, this corresponds to the logical operation that is commonly called "exclusive disjunction" and that is otherwise expressed as "x or y, but not both" .  Depending on the context, other signs and readings that invoke this operation are:  "x ? y", read as "x is not equal to y" or as "exactly one of x and y", and "x <?> y", read as "x is not equivalent to y" or as "x opposes y".

The "sum" of x and y, for values x, y ? B, is presented in Table 9.  Viewed as a function of logical values, + : B?B �> B, this corresponds to the logical operation that is commonly called "exclusive disjunction" and that is otherwise expressed as "x or y, but not both" .  Depending on the context, other signs and readings that invoke this operation are:  "x ? y", read as "x is not equal to y" or as "exactly one of x and y", and "x <?> y", read as "x is not equivalent to y" or as "x opposes y".

As a purely informal aid to interpretation, I frequently use the letters "p", "q", and "P", "Q" to denote propositions.  This can serve to tip off the reader that a function is intended as the indicator function of a set, and thus it saves the trouble of declaring the type f : U �> B each time that a function is introduced as a proposition.

As a purely informal aid to interpretation, I frequently use the letters "p", "q", and "P", "Q" to denote propositions.  This can serve to tip off the reader that a function is intended as the indicator function of a set, and thus it saves the trouble of declaring the type f : U �> B each time that a function is introduced as a proposition.

Another convention of use in this context is to let underscored letters stand for k�tuples or sequences of objects.  Typically, the objects are all of one type, and typically the letter that is underscored is the same basic character that is indexed or subscripted, as in a list, to denote the individual components of the k�tuple or sequence.  For instance:

Another convention of use in this context is to let underscored letters stand for k-tuples or sequences of objects.  Typically, the objects are all of one type, and typically the letter that is underscored is the same basic character that is indexed or subscripted, as in a list, to denote the individual components of the k-tuple or sequence.  For instance:

1. If v1, ..., vk ? V, then v = <v1, ..., vk> ? V' = Vk.

1. If v1, ..., vk ? V, then v = <v1, ..., vk> ? V' = Vk.