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Table 1 Truth table for (μ1 = μ2) and its logical equivalent

From: A logical analysis of null hypothesis significance testing using popular terminology

μ1 = μ2 (\(\overline{x}\) 1\(\overline{x}\) 2) due to chance alone (\(\overline{x}\) 1\(\overline{x}\) 2) not due to chance alone {(μ1 = μ2) [(\(\overline{x}\) 1\(\overline{x}\) 2) due to chance alone]} {(μ1 = μ2) [(\(\overline{x}\) 1\(\overline{x}\) 2) not due to chance alone]} ({(μ1 = μ2) [(\(\overline{x}\) 1\(\overline{x}\) 2) due to chance alone]} {(μ1 = μ2) [(\(\overline{x}\) 1\(\overline{x}\) 2) not due to chance alone]} )
T T F T F T
T F T F T T
F T F F F F
F F T F F F