Part 2: Consider the partial order with domain {3, 5, 6, 7, 10, 14, 20, 30, 60} and with z < y if z evenly divides y. Select the correct Hasse diagram for the partial order. 14 10 (iii) (i) Figure 4: A Hasse diagram shows a set of elements, 3, 5, 6, 7, 10, 14, 20, 30, and 60. The elements are arranged as follows: 3 at the bottom; 6 is placed vertically above 3; 5 is placed to the right and little above 3; 10 is placed vertically above 5; 7 is placed to the right of 5 but little above 10; 30, 20, 10, and 60 are placed in a diamond together, and 60 is placed at the top. The vertical line segments between the elements are as follows: 3 and 6, 6 and 30, 5 and 10, and 7 and 14. The inclined line segments between the elements are as follows: 10 and 30, 10 and 20, 30 and 60, and 20 and 60. Figure 2: A Hasse diagram shous a set of elements, 3, 5, 6, 7, 10, 14, 20, 30, and 60. The elements are arranged as follows: 3, 6, and 30 are arranged vertically one above another, connected by vertical line segments; 5 and 20 are arranged vertically one above another to the right of 3 and 6, respectively, connected by a vertical line segment; 10 is placed inclined up to the right of 20, horizontally aligned with 30, and 60 is placed above 30 and 10, vertically aligned with 20; at the top; inclined line segments connect 10 and 30, 30 and 60, 60 and 20, 20 and 5, 5 and 10, and 5 and 30 to form a diamond shape; and 7 and 14 are placed to the right of 5 and 10, respectively, connected by a vertical line segment.

Find an increasing subsequence of maximal length and a decreasing subsequence of maximal length in the se- quence 22, 5, 7, 2, 23, 10, 15, 21, 3, 17.

Here are some set definitions that we will refer to in the exercises of this assignment. A={ 1, 3, 5, 7,9} • B={x| (x ≥ 1) ^ (x ≤ 9) } • C= {x| (x A) ^ (x = B) } • D={x| (vy)(x*y = y)} • E= {x|(3y)(x*y=y)} For each statement below, answer whether the statement is true or false, and briefly explain why. 1. 3€ A 2. 4€ A 3. 3 € B 4. 4 € B 5. 3 € C 6. 4 € C 7. CC B 8. BCC [ S 9. DcA 10. ECD G D C A D = I can give you any inteyen and call it x. Each x I give you has a y, so that for all Values of yx*y = y x=3 x=5 X= 7 X |Y LY|XOY X: = XIXI хочу |-||-|| Te و ال 13 Fol نعاما X= | 3 Since X Y X+Y 3-1 3 3 212 313 e- for all 1 the only this this is 3 bの 6 y x.. 5-4-574 0070 5 171 2 10 72 315 23 کی Š 5 5 хса alm X Y xey 9 T -q 90 00 9 9 18 9222 time the relation is true is when is false as it would need to be true in the set members

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