R a b A1 B1 A2 B2 A3 B1 A1 B2 A2 B2 A3 B2 A1 B4 A2 B4 S A A1

R

a

b

A1

B1

A2

B2

A3

B1

A1

B2

A2

B2

A3

B2

A1

B4

A2

B4

S

A

A1

A3

T

B

B2

B4

Please indicate which of the following statement is correct?

a. Table R can be divided by Table S

b. Table R can be divided by Table T

c. Both A and B are correct

d. Neither A nor B is correct

a	b
A1	B1
A2	B2
A3	B1
A1	B2
A2	B2
A3	B2
A1	B4
A2	B4

Solution

Given, Relation R, S, and T.

Now, R divided by S:

R/S = (A, B / A) = B

So,

In above,

A1 has B: B1, B2, B4

A3 has B: B1, B2

B1, B2 are common in both A1 and A3, So the resultant relation has tuples B1 and B2.

Now, R divided by T:

R / T = (A, B / B) = A

So,

In above,

B2 has A: A1, A2, A3

B4 has A: A1, A2

A1, A2 are common in both B2 and B4, So the resultant relation has tuples A1 and A2.

Now, From above, It is clear that,

a. Table R can be divided by Table S

and

b. Table R can be divided by Table T

So, c. Both A and B are correct.

So, the answer is c. Both A and B are correct.

B

B1

B2