Answer to Question #309144 in Discrete Mathematics for blaize

Question

38)

Let 𝐴 = {2,3,4,5,6,7,8,9} and define an order relation ∼ on 𝐴 by the following: For all 𝑎, 𝑏 ∈ 𝐴, 𝑎 ∼

𝑏 if, and only if, there exists an integer 𝑡 such that 𝑏 = 𝑡𝑎. Then, in the poset (𝐴, ∼)

A) The minimal elements are 2 and 3 and the maximal elements are 6, 8 and 9.

B) The minimal elements are 2, 3, 4 and 5 and the maximal elements are 6, 7, 8 and 9.

C) There are no minimal elements, nor any maximal elements.

D) The minimal elements are 2, 3, 5 and 7 and the maximal elements are 5, 6, 7, 8 and 9.

39)

Let 𝐴, 𝐵, 𝐶 and 𝐷 be sets, and let 𝑅 ⊆ 𝐴 × 𝐵, 𝑄 ⊆ 𝐵 × 𝐶 and 𝑃 ⊆ 𝐶 × 𝐷 be relations. Then the

relations (𝑅 ∘ 𝑄) ∘ 𝑃 and 𝑅 ∘ (𝑄 ∘ 𝑃), from 𝐴 to 𝐷

A) must not be equal.

B) are sometimes equal, and sometimes not, depending on the sets 𝐴, 𝐵, 𝐶,𝐷 and the relations 𝑅, 𝑄

and 𝑃.

C) must be equal.

D) are not defined

Answer 1

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