$($OB$/21/2024-12)$

and operators $[$hint: if there is a horseshoe or conditional $($if$,$ then; on the condition that; implies that; only if; etc.$),$ make sure you are placing them in the right order$-$you can double check the list in the book$]$:

Either Fiat improves mileage and Toyota closes a factory or Honda reduces inventory.

Hints for Translating Sentences Into Symbolic Statements:

Identify the variables: Look for key elements or variables in the sentence. Take the first letter $($like $"$C$"$ for "Cosmo raises its prices"$)$ and assign them to each.

Use the connectives: Pay attention to words like "and" $($conjunction$),"$or$"($disjunction$),$ "not" $($negation$),$ and $"$if$...$then" $($implication$).$ They indicate how different statements are related. Also, review the charts in MindTap that detail synonyms that work the same as these connectlves $($Hurley$,6\mathrm{.}1$; also, on the syllabus under Topic Summary$)$:

Apply logical operators: Use logical operators $($e$.$g$.,$ for "and," v for $"$or$,"$ for "not," sup for $"$if$...$then," $-=$ for $"$if and only if$")$ to connect your atomic propositions based on the sentence structure.

Parentheses matter: Use parentheses to clarify the order of operations. They help ensure your statement is unambiguous.

Doublecheck for negations: Watch out for negations $($e$.$g$.,$ "not" or $"$it is not the case that"$)$ in the sentence and apply them correctly to your propositions.

teboard$)$

F $*$ TVH

$(FvvT)*H$

$FvvT*H$

$F*(TvvH)$

$(F$@$T)vvH$