Question 178385: I have just read a section on functions and mapping. They discussed injective, surjective and bijective mapping. I understand the first two but am having difficulty understanding bijective mapping. Please explain with example.
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! For injective, at MOST one element from the first set is mapped to every element in the second set (if A = {1, 2, 3} and B = {4, 5, 6}, an injective mapping can give you the pairs (1,4) and (2,6). Notice nothing is mapped to 5, so it's not surjective.). For surjective, at LEAST one element from the first set is mapped to every element in the second set (if A = {1, 2, 3} and B = {4, 5, 6}, a surjective mapping can give you the pairs (1,4), (2,4), (3,5), and (3,6). Notice 1 and 2 are both mapped to 4, so it is not injective.). For bijective, EXACTLY one element from the first set is mapped to every element in the second set (if A = {1, 2, 3} and B = {4, 5, 6}, a bijective mapping can give you the pairs (1,4), (3,5), and (3,6)). Notice that every bijective function is also injective and surjective.
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