How many elements does the successor of a set with n elements have?Sometimes the number of times that an element occurs in an unordered collection matters, Multisets are unordered collections of elements where an element can occur as a member more than once. The notation (m1 a1, m2 a2,....,mr ar} denotes the multiset with element a1 occurring m1 times, element a2 occurring m2 times, and so on. The numbers mi, i = 1, 2,....,r are called the multiplicities of the elements ai, i = 1, 2,....,r.Let P and Q be multisets. The union of the multisets P and Q is the multiset where the multiplicity of an element is the maximum of its multiplicities in P and Q. The intersection of P and Q is the multiset where the multiplicity of an element is the minimum of its multiplicities in P and Q. The difference of P and Q is the multiset where the multiplicity of an element is the multiplicity of the element in P less its multiplicity in Q unless this difference is negative, in which case the multiplicity is 0. The sum of P and Q is the multiset where the multiplicity of an element is the sum of multiplicities in P and Q. The union, intersection, and difference of P and Q are denoted by P ? Q. P ? Q, and P – Q. respectively (where these operations should not be confused with the analogous operations for sets). The sum of P and Q is denoted by P + Q.

SOLUTIONStep 1The successor of a set A is defined as Thus we can see that we are adding the set A to the set A.ie for example consider Therefore the successor Thus we are adding one more element to the original set .Therefore the successor of a set with n elements has n+1 elements.