A predicate is a logical expression. In the context of set theory, usually a predicate is a statement which can be expressed using only symbols from symbolic logic, variables, and the set-theoretic relations and .
In English, this predicate reads, "The empty set is an element of ." Note that this is not true for all sets.
In English, this translates to, "For all sets , the empty set is a subset of ." Since is an abbreviation for the predicate , this can be rewritten using only logical symbols, variables, and the set-theoretic notations and , as follows:
In English, this revised predicate reads, "For all sets , for all sets , if is an element of the empty set, then is an element of ."
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