We are given the following sets
A = {January, June, July}
D = {March, May, June}
F = {May, June, July}
We are asked to find the following
a. D - F
b. F - D
c. (A ∪ D) - F
a. D - F
We have to subtract the set F from the set D
D - F = {March, May, June} - {May, June, July}
D - F = {March}
b. F - D
We have to subtract the set D from the set F
F - D = {May, June, July} - {March, May, June}
F - D = {July}
c. (A ∪ D) - F
First, let us find the union of set A and D
A ∪ D = {January, June, July} ∪ {March, May, June}
A ∪ D = {January, March, May, June, July}
Now we have to subtract the set F from (A ∪ D)
(A ∪ D) - F = {January, March, May, June, July} - {May, June, July}
(A ∪ D) - F = {January, March, May}
Therefore, the results are
D - F = {March}
F - D = {July}
(A ∪ D) - F = {January, March, May}