For example, the equivalence class of a line for the relation "is parallel to" consists of the set of all lines parallel to it.
For example, demonstrating equivalence with a known risk of 0.01, a 20% maximal risk difference, and a one-sided test (α = 0.05 and β = 0.2) requires: under the one-group design (known risk), 15,309 patients; and under the two-group design, 30,617 patients per group.
For example, an equivalence class with cell t[B] is merged with the one with cell (t'[B]) based on (phi _1 : A rightarrow B), then an equivalence class with cell t[C] is merged with the one with (t'[C]), based on another rule (phi _2: B rightarrow C), and so on.
The assumption is that other tests show, for example, potential equivalence to statistical significance.
For example, should equivalence intervals reflect the fact that reference varieties are likely to perform differently at different locations?
Thus, annihilation is an example of the equivalence of mass and energy and a confirmation of the theory of special relativity, which predicts this equivalence.
The more important logical relations are implication (as in the first example above) and equivalence; and, as displayed in the square of opposition (see opposition, square of), contrariety (as in the second example), contradiction, subcontrariety, and subimplication.
We are able to predict the phase between the mass flow rate oscillations and the resulting heat release fluctuations, as function of the operating conditions, for example, the mean equivalence ratio and mass flow rate.
John Rennie, the former editor in chief of Scientific American, has posted a strong criticism of my piece as a glaring example of false equivalence — particularly my characterization (which I added after the original post) of the chart of "climate alarmism" machinery.
The identity relation on any set $A$ is the paradigmatic example of an equivalence relation.
