The answers to exercises marked [BB] can be found in the Back of the Book.[BB] What is wro...

The answers to exercises marked [BB] can be found in the Back of the Book.

[BB] What is wrong with the following argument, which purports to prove that a binary relation that is symmetric and transitive must necessarily be reflexive as well?

Suppose R is a symmetric and transitive relation on a set A and let a ∈ A. Then, for any b with (a, b) ∈ , we have also (b, a) ∈ by symmetry. Since now we have both (a, b) and (b, a) in , we have (a, a) ∈ ft as well, by transitivity. Thus, (a, a) ∈ , so R is reflexive.