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Question 9

Which of the following relations on the set {1, 2, 3, 4} is antisymmetric?

Question 10

Question 1 (1 point Among the choices listed, which one pair of fields (or column headings) could not constitue a composite key for the below? Part number Project Quantity Color code 1001 1092 1101 3477 25 4975 6984 4 10 1 9048 9191 2 80 4 O Project, Color code O Quantity, Color code O Project, Quantity O None, all the listed pairs could serve as a composite key.

Explanation / Answer

(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)

4. R1 = { (3,1),(1,3),(4,1),(2,2) }

Please note that (4,1) exists but (1,4) does not and (3,1) and (1,3) both exist. Thus R1 is neither symmetric nor antisymmetric.

However (1,3) and (3,1) exist but (3,3) does not. So R1 is not transitive.

Therefore the first statement i.e R1 is transitive is false.

5. (1,1), (4,2), (16,4)

Note that 1 = 12, 4 = 22 and 16 = 42

R = {(x,y) | x = y2}

8. { (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,4), (4,4) }

This relation is not irreflexive as (4,4) exists.

{ (1,1), (1,2), (2,1), (2,2) }

This relation is not irreflexive as (1,1) exists.

{ (2,4), (4,2), (1,3), (3,1) }

As none of (1,1), (2,2), (3,3) and (4,4) exist, this relation is irreflexive and is the answer.

(The last option contains (1,1) and is therefore not irreflexive)

9. { (1,2), (1,3), (1,4), (2,3), (2,4), (3,4), (4,1), (4,4) }

This relation is not antisymmetric as (1,4) and (4,1) both exist.

{ (1,1), (1,2), (2,1), (2,2) }

This relation is not antisymmetric as (1,2) and (2,1) both exist.

{ (2,4), (4,2), (1,3), (3,1) }

This relation is not antisymmetric as (1,3) and (3,1) both exist.

{ (1,1), (1,2), (2,2), (2,3), (3,3), (3,4), (4,4), (4,1) }

This relation is antisymmetric as there is no pair (x,y), (y,x) where x and y are not the same.

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