Answer
The statement is true.
Work Step by Step
$(c-3)+3=(c+(-3))+3 \qquad $(definition of subtraction)
$=c+((-3)+3) \qquad $(associative property of addition)
$=c+0\qquad $(inverse property of addition)
$=c \qquad $(identity property of addition)
(LHS = RHS)
The statement is true.