Question

This is database design class, I can't solve part 3 and part 4

3. Use Armstrong's Axioms to show that if F={A->B, C>D}, F logically implies AC->BD. (20 points) 4. Consider a relational schema R=ABCDEGHI, and the following set of functional dependencies: F={A->BC,B=>CD,DE->GH} a) Find A+. Show your work. (10 points) b) Find AE+. Show your work. (10 points) c) Find BGH+. Show your work. (10 points)

can you please help me?

Thank you

Answer 1

If A golds B and C holds D then ABàCD

Proof:-

1. AàB (given)

2. CàD (given)

3. ACàBC (Augmentation of 1 and C)

4. AC → B (Decomposition of 3)

5. AC → AD (Augmentation of 2 and P)

6. AC → D (Decomposition of 5)

7. AC → BD (Union 4 and 6)

2)

R=ABCDEGHI

F={AàBC,BàCD,DEàGH}

a) A+

{A+ = ABCD}

You can find BC from A and CD from B so final closer is ABCD

b) AE+

AE+ = ABCDEGH

         = R

   You can find BC from A

   CD from B

And GH from AE

so final clouser of AE+ is ABCDEGH

c) BGH+

BGH+ = BCDGH

BGH is given left side and

You can find CD from B

so final clouser of BGH+ is BCDGH.