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Discrete Mathematics and Combinatorics by T. Sengadir

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Chapter 2

 

1. In general, f(AB) = f(A) ∩ f(B). Suppose yf(A) ∩ f(B). This implies that y = f(A) for some aA and y = f(B) for some bB. From this, we cannot conclude that y = f(x) for some xAB. Hence the equality is not valid in (ii).

2 In this section, the reader might feel that certain obvious results are proved in a roundabout manner. But the point is that although the results are obvious and intuitively clear, their proofs need to be rigorous.

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