Are the intersection of any two half-planes necessarily a half-plane

Question

Keira Vasquez

Chemistry

20 February, 23:39

Are the intersection of any two half-planes necessarily a half-plane

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Answers (1)

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Bryanna Avila · Answer 1

Answer;

The answer is No,

Explanation;

-The intersection of two parallel half-planes A and B is either a half-plane (either A or B, when A and B have similar orientation) or the empty set (when A and B have opposite orientation).

-When A and B are not parallel, their intersection is a maximal open region bounded by the two lines that define A and B, respectively. In this case, the intersection always exists and it is never a half-plane.