Find A one-one mapping from A to B

Question

1.Given A={2,3,4},B={2,5,6,7}, construct an example of each of the following .

i)A one-one mapping from A to B

ii)A mapping from A to B which is not one-one

iii)A mapping from B to A

2. check whether {(x,y):x is a person, y is the mother of x} is a function or not

Answer 1

1

(i) b=a+3 maps {2,3,4} in A (all of A) to {5,6,7} in B. It doesn't matter that 2 in B is not mapped.

(ii) b=a+2 maps 3 and 4 in A to 5 and 6 in B, but 2 does not map to B,

(iii) a=b-3 maps 5, 6 and 7 in B to 2, 3 and 4 in A but fails to map 2.

2 This function implies that x=f(x,y), which implies x=f(f(x,y),y), which implies x=f(f(f(x,y),y),y) and so on. The "function" is mapping back into itself iteratively, recursively and indefinitely. It cannot be a function.