Review the formal language ADD from Exercise $1\mathrm{.}2\mathrm{.}2$ from Chapter $1.$ For each statement below, indicate whether that statement

concerns the syntax of ADD, or the semantics of ADD. $($If it helps,

think of the models of ADD as sets of integers together with the

usual facts about addition as applied to integers.$)$ Explain your

answers. $($Do not worry about whether the following statements

are true or false, but only whether they assert something about

syntax, or semantics.$)$

$($a$)$ Some wffs of ADD do not contain the symbol $+.$

$($b$)$ A wff of ADD is true iff it expresses an arithmetic truth.

$($c$)$ Let$$s say that a wff of ADD is $$zeroful$$ iff it contains more zeros

than any other symbol. Then the wff $00010$ is zeroful but the

wff $11101$ is not zeroful.

$($d$)$ Let$$s say that a wff of ADD is $$largish$$ iff it expresses a number

greater than one hundred. Then $111$ and $99+7$ are largish, but

$001$ and $2+7$ are not largish.

The statements that you are evaluating

for questions $($c$)$ and $($d$)$ are those made

by the final sentence in each case.

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