Redundance of logic 'and' in definition of preference relation

Question

Let $(a,b), (a',b') \in \mathbb R^2$. I came across the following definition of a preference relation $\succeq$ \begin{align} (a,b) \succeq (a',b') \quad \text{iff} \quad [a > a' \text{ and/or } b < b'] \text{ or } [a = a' \text{ and } b = b']. \end{align} And I was wondering if the 'and' in 'and/or' is redundant, because if $a > a' \text{ and } b < b'$ then $a > a' \text{ or } b < b'$.

Answer 1

While the logical $\lor$ is clearly defined as an inclusive or, it is not always clear if the English use of 'or' is inclusive or exclusive.

Some people will say that we use 'either ...' ...' if we want to express an exclusive or, but you can;t really go by that either. For example, if the waietr in a restaurant asks whether you want 'soup or salad' with your meal, it's clear that you can't have both. And if I say that when I grow old, I want to be 'either rich or happy', I really don't mind if I turn out both rich and happy.

So, to avoid confusion, many people will use 'and/or' to try and express that an inclusive or is meant. I am sure that's what's happening here as well.