From Perloff, Microecomics, 6th edition (Pg. 75):
A consumer chooses between bundles of goods by ranking them as to the pleasure the consumer gets from consuming each. We summarize a consumer’s ranking using a preference relation, such as the consumer weakly prefers Bundle a to Bundle b, if the consumer likes Bundle a at least as much as Bundle b.
Given this weak preference relation, we can derive two other relations. If the consumer weakly prefers Bundle a to b, but the consumer does not weakly prefer b to a, then we say that the consumer strictly prefers a to b—would definitely choose a rather than b if given a choice—which we write as a b.
If the consumer weakly prefers a to b and weakly prefers b to a —— then we say that the consumer is indifferent between the bundles, or likes the two bundles equally.
My question is: When you have declared that a consumer weakly prefers A to B, how could you then argue that a consumer could also prefer (weakly) B to A? Aren't they mutually exclusive?