Question

Give a mathematical example to show the following:

For any rational number m/n and any positive real number a, a^(-m/n) means 1/a^(m/n).

Answer 1

The expression (Y⋂X')⋃Z' evaluates to {1, 3, 4}.

Step-by-step explanation:

To find (Y⋂X')⋃Z', we first need to compute X', the complement of set X. Since U is the universal set, X' = U - X. Substituting the values, X' = {1, 3, 4}. The intersection of Y and X' (Y⋂X') is then {4, 5, 6} ∩ {1, 3, 4}, which simplifies to {4}. Moving on, Z' is the complement of set Z, so Z' = U - Z, resulting in Z' = {1, 5, 6}. Finally, the union of {4} and Z' ({4}⋃{1, 5, 6}) gives us the set {1, 3, 4}, which is the solution to the expression (Y⋂X')⋃Z'.

In summary, the process involves finding the complements of sets X and Z, determining the intersection of Y and X', and then taking the union of the result with Z'. The final set {1, 3, 4} represents the elements that satisfy the given expression in the context of the universal set U and the sets X, Y, and Z provided.