Logical formulas.

Write a logical formula that is true if and only if the described condition is true. For example,

if the description is \A, B, and C are all true, but D is not," you would write A^B ^C ^:D. Use

^, _, and : for AND, OR, and NOT.

iv. At least one member of each group must be true: group 1 contains A, B, and C, group 2

contains D, E, and F, and group 3 contains A, F, and G. (Thus if A is true, it satises the

requirement for both group 1 and group 3.)

v. Exactly one of A, B, or C is true.

vi. At least one of A, B, or C is false. Do not use _ (OR).