State inclusion-exclusion principle. For which number x is true that\[\lfloor x \rfloor = \lceil x \rceil\] ?Let f and g be functions from {1, 2, 3, 4} to {a, b, c, d}, and from {a, b, c, d} to {1, 2, 3, 4}, respectively with f(1) = d, f(2) = c, f(3) = a, and f(4) = b, and g(a) = 2, g(b) = 1, g(c) = 3 and g(d) = 2.

• a. If f and g one-to-one?
• b. If f and g on-to?
• c. Does either f or g have an inverse? If so find this inverse.