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Which of the following digraphs G = (V, E) are acyclic? Give full explanation. In each...

  1. Which of the following digraphs G = (V, E) are acyclic? Give full explanation. In each description given below,

    assume x ∈ V, y ∈ V .

    1. (i) V is the set of positive integers, and (x,y) ∈ E if and only if x is a divisor of y;

    2. (ii) V isasetofsize4and(x,y)∈Eforeveryx,y;

    3. (iii) V is the set of positive integers, and (x, y) ∈ E if and only if y is divisible by a higher power of 2 than x is;

    4. (iv) V is the set of Amherst streets and (x, y) ∈ E if x and y intersect

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