#### Answer

a. (p∧q)∧r
b. p∧~q
c. p∧(~q∨~r)
d. ~p∧q∧~r
e. ~p∨(q∧r)

#### Work Step by Step

Observe that each statemnent has two possibilities. (1) Either "DATAENDFLAG is off" or "DATAENDFLAG is on." (2) Either "ERROR equals 0" or "ERROR does not equal 0." (3) Either "SUM is less than 1,000" or "SUM is greater than or equal to 1,000." Thus, negating the former implies the latter. Always use parentheses to break up statements containing "∧" or "∨," and remember that "~" is computed in the order of operations before "∧" or "∨" unless the order is overridden by use of parentheses.