Given that α, β, and γ are three distinct planes, consider the following propositions: - Proposition p: If α⊥β and β⊥γ, then α∥γ. - Proposition q: If three non-collinear points on plane α are equidistant from plane β, then α∥β.
Among the following conclusions, the correct one is
Pick one
Solution
Since when α⊥β and β⊥γ, it is possible for α to be parallel or perpendicular to γ, the proposition p is a false proposition. Furthermore, if three non-collinear points on plane α are equidistant from plane β, it is possible for α and β to be parallel or intersecting. Therefore, proposition q is also a false proposition. Consequently, the proposition "p and q" is false, the proposition "p or not q" is true, the proposition "p or q" is false, and the proposition "not p and not q" is true. Therefore, the correct choice is C.
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Source: NuminaMath-1.5,
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