Given that set $A$ has 42 elements and set $B$ has 24 elements, determine each of the following (a) The maximum possible number of elements in $A \cup B$ elements (b) The minimum possible number of elements in $A \cup B$ elements (c) The maximum possible number of elements in $A \cap B$ elements (d) The minimum possible frumber of elements in $A$ $\cap B$ elements

Step 1 ：Given that set $A$ has 42 elements and set $B$ has 24 elements, we are asked to determine the maximum and minimum possible number of elements in the union and intersection of these two sets.

Step 2 ：The maximum possible number of elements in the union of two sets $A$ and $B$ is the sum of the number of elements in both sets, assuming that there are no common elements between the two sets. Therefore, the maximum possible number of elements in $A \cup B$ is $42 + 24 = \boxed{66}$.

Step 3 ：The minimum possible number of elements in the union of two sets $A$ and $B$ is the number of elements in the larger set, assuming that all elements of the smaller set are also in the larger set. Therefore, the minimum possible number of elements in $A \cup B$ is $\boxed{42}$.

Step 4 ：The maximum possible number of elements in the intersection of two sets $A$ and $B$ is the number of elements in the smaller set, assuming that all elements of the smaller set are also in the larger set. Therefore, the maximum possible number of elements in $A \cap B$ is $\boxed{24}$.

Step 5 ：The minimum possible number of elements in the intersection of two sets $A$ and $B$ is zero, assuming that there are no common elements between the two sets. Therefore, the minimum possible number of elements in $A \cap B$ is $\boxed{0}$.