If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find

1.	If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find the set of ordered pairs such that 'a' is factor of 'b' and a < b.
Answer» Since, A = {2, 4, 6, 9} B = {4, 6, 18, 27, 54}, we have to find a set of ordered pairs (a, b) such that a is factor of b and a < b. Since, 2 is a factor of 4 and 2 < 4. So, (2, 4) is one such ordered pair. Similarly, (2, 6), (2, 18), (2, 54) are other such ordered pairs. Thus the required set of ordered pairs is {(2, 4), (2, 6), (2, 18), (2, 54), (6, 18), (6, 54,), (9, 18), (9, 27), (9, 54)}.

If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find the set of ordered pairs such that 'a' is factor of 'b' and a < b.

Answer»

Since, A = {2, 4, 6, 9}

B = {4, 6, 18, 27, 54},

we have to find a set of ordered pairs (a, b) such that a is factor of b and a < b.

Since, 2 is a factor of 4 and 2 < 4.

So, (2, 4) is one such ordered pair.

Similarly, (2, 6), (2, 18), (2, 54) are other such ordered pairs. Thus the required set of ordered pairs is

{(2, 4), (2, 6), (2, 18), (2, 54), (6, 18), (6, 54,), (9, 18), (9, 27), (9, 54)}.