let A 01234X012 let B n n is a positive factor of 144 and l

let A ={0,1,2,3,4}X{0,1,2}, let B = {n| n is a positive factor of 144}, and let f: AB with f(a1, a2) = 2^a1·3……Is f one-to-one? Onto?

Solution

The function is one-one if there is only one number mapping to the space

2^0 * 3 = 3,is a factor of 144

2^1 * 3 = 6, is a factor of 144

2^2 * 3 = 12, is a factor of 144

2^3 * 3 = 24, is a factor of 144

2^4 * 3 = 48, is a factor of 144

Since all the numbers in A are convered, hence the function is onto

The function is not one-one, since there are huge number of mappings from one number to the B, hence the set is not one-one

Therefore, the function is not one-one but onto