A B a b a A b B A B a b a multiply by b a A b B For

A + B = {a + b | a A, b B}

A * B = {a * b (a multiply by b) | a A, b B}

For example, if A is {2,3} and B is {4,5}, then A + B = {6,7,8} and A * B = {8,10,12,15}

describe the following sets:

(a) N+ + N+

(b) N+ * N+

Where N – set of natural numbers, N = {0,1,2,…} and N + = N \\ {0} = {1,2,3,…}.

Solution

(a) (N+) + (N+) = (N+) \\ {1}

Sum of two Natural number results in a natural number as well . Since , we have to add {1} with smallest element , which is {1} , it would result as smallest element of resulting set to be {2}

(b) (N+) * (N+) = (N+)

Product of two Natural Numbers would be a natural number and the smallest element which can be generated would be {1}