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If f:A→B is a bijective function and n(A)=6 then which of the following is not possible*Number of elements in range of f is 6n(A)=n(B)n(B)=6n(B)=8

Question

If f:A→B is a bijective function and n(A)=6 then which of the following is not possible?

  • Number of elements in range of f is 6
  • n(A)=n(B)
  • n(B)=6
  • n(B)=8
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Solution

The statement that is not possible is "n(B)=8".

Here's why:

  1. A bijective function, also known as a one-to-one correspondence, is a function where every element of the set A has a unique image in set B, and every element of set B has a unique pre-image in set A.

  2. Given that f:A→B is a bijective function and n(A)=6, this means that there are 6 elements in set A.

  3. Because f is bijective, this means that there must also be exactly 6 elements in set B. This is because every element in A must map to a unique element in B, and vice versa.

  4. Therefore, the number of elements in the range of f is 6, n(A)=n(B), and n(B)=6 are all possible.

  5. However, n(B)=8 is not possible, because this would mean that there are 8 elements in set B. This contradicts the fact that f is a bijective function and there are only 6 elements

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