In a Hasse diagram of a poset (𝐴, ≤), a pair of distinct elements 𝑎 and 𝑏 of 𝐴 are connected by a line
segment if, and only if,
A) either 𝑎 ≤ 𝑏 and there is no 𝑐 ∈ 𝐴 such that 𝑎 ≤ 𝑐 ≤ 𝑏, or else 𝑏 ≤ 𝑎 and there is no 𝑐 ∈ 𝐴 such
that 𝑏 ≤ 𝑐 ≤ 𝑎.
B) either 𝑎 ≤ 𝑏 or else 𝑏 ≤ 𝑎.
C) 𝑎 ≰ 𝑏 and 𝑏 ≰ 𝑎.
D) 𝑎 ≤ 𝑏.
Much appreciate!
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