Final answer:
Given ~a = b, by the principle of symmetry or flip-over operation (reflexive symmetry), the inferred relationship would be -a = ~b, where the '~' symbol represents the 'NOT' operation in logical mathematical expressions.
Step-by-step explanation:
In the realm of logic and mathematics, if we have a given that ~a = b, inferring something by symmetry would mean flipping around the elements while maintaining the equivalent relation. Thus, the inferred relationship in this context would be -a = ~b.
This concept is inspired by a type of symmetry known as 'reflexive symmetry', where a flip-over operation takes place. Such a relation in this logical context suggests an equivalent transformation of the elements.
It is important to understand that each mathematical symbol carries significant meaning. The '~' symbol is often used to represent the 'NOT' operation in logic based mathematics. Therefore, in the context of the given logic statement, when we infer by symmetry, we are flipping the relationship and thus the statement becomes -a = ~b.
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