Question

Consider the tables You may assume the corresponding columns have the same domains

T1

D	E	F
10	a	5
15	b	8
15	c	4
25	a	6

T2

A	B	C
10	b	6
25	c	3
10	b	5

Show the results of each of the following relational algebra expressions in terms of table:

i. T1 ⋈ (D = A) T2

ii. T1⋈ (E=B) T2

iii. T1∪T2

iv. T1–T2

v. π (D,E)(T1) / π (B) (T2)

Answer 1

T1 :

D	E	F
10	a	5
15	b	8
15	c	4
25	a	6

T2:

A	B	C
10	b	6
25	c	3
10	b	5

i)
This will return the rows in which column D and A have equal values after doing the cross product

D	E	F	A	B	C
10	a	5	10	b	6
10	a	5	10	b	5
25	a	6	25	c	3

ii)  
This will return the rows in which column E and B have equal values after doing the cross product.

D	E	F	A	B	C
15	b	8	10	b	6
15	b	8	10	b	5
15	c	4	25	c	3

iii)
Append the rows of T2 after T1 to get the union of two tables

D	E	F
10	a	5
15	b	8
15	c	4
25	a	6
10	b	6
25	c	3
10	b	5

iv)
Subtract the rows from T1 that are same in T2

There are no similar rows in both the tables. So T1 - T2 is the same as T1

D	E	F
10	a	5
15	b	8
15	c	4
25	a	6

v)
In this express there are two terms.
We analyze them separately

gives columns D and E from T1

D	E
10	a
15	b
15	c
25	a

gives column B from T2

B

b

c

We have to divide these two tables. Dividing means giving those values of T1(D) which are occurring with every value of T2(B) in T1
In T1, 10 occurs with a not with b and c.
15 occurs with both b and c. So it will be in the output
25 occurs with a.

So, the output of the given expression will be

D

15

Hope this helps
If you have any doubt feel free to comment
Thank You!!