Draw the Hasse diagram for a poset P satisfying the following conditions (and justify that they are satisfied): • Pis graded. • P is not rank-unimodal. (Note that a poset satisfying po ≤ P ≤ --- < Pa or Po≥ P₁ ≥ 2 Pa is considered to be rank-unimodal). • P is not rank-symmetric. • P does not satisfy the Sperner property. • There does not exist a poset P' satisfying the first 4 conditions whose rank is smaller than the rank of P. For any added challenge, find (with proof) the minimal order (number of elements) of a poset satisfying these conditions.

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A: The correct option is A .i.e. {9, 10, 11, 12, 13, 14, 15}

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Q: II. (Vz € N)(3: € Q)(zz = y) III. 1-1+1-1+..= 0. VI. 7+25 mod 16.

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Q: Let U= (1,2,3, ...,20}. Write the following sets by listing the elements in braces. (a) {xEU|x is…

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Q: raw the Hasse di

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