Question

Let A = {l, m, m, m, n, n, n, p, p, p} and B = {l, l, m, n, n, n, p, r, r}, find the operations of the following multisets:

A. A + B 

B.  A - B 

C. A U B

D.  A ∩ B

Answer 1

A. The sum of two multisets A and B, is a multiset such that the multiplicity of an element is equal to the sum of the multiplicity of an element in A and B

$$A+B$$

$$=\{l,l,l,m,m,m,m,n,n,n,n,n,n,p,p,p,p,r,r\}$$

B. The difference of two multisets A and B, is a multiset such that the multiplicity of an element is equal to the multiplicity of the element in A minus the multiplicity of the element in B if the difference is positive, and is equal to 0 if the difference is 0 or negative

$$A-B$$

$$=\{m,m,p,p\}$$

C. The Union of two multisets A and B is a multiset such that the multiplicity of an element is equal to the maximum of the multiplicity of an element in A and B

$$A\cup B$$

$$=\{l,l,m,m,m,n,n,n,p,p,p,r,r\}$$

D. The intersection of two multisets A and B, is a multiset such that the multiplicity of an element is equal to the minimum of the multiplicity of an element in A and B

$$A\cap B$$

$$=\{l,m,n,n,n,p\}$$