Question

QI.

Answer 1

What we're trying to do here is pairing elements of A with elements of B, and the rule for pairing them is that the least common multiple must be 2.

We can't use zeroes, because every multiple of 0 is still 0.

We can't either use numbers greater than 2, because their multiples will be greater than 2.

After this trimming, we're left with the following subsets:

$\hat{A}=\{1,2\},\quad \hat{B}=\{1,2\}$

So, the possible couples are:

$(1,1),\quad (1,2),\quad (2,1),\quad (2,2)$

The first couple is obviously not good, because the least common multiple of 1 and 1 is 1.

The other three are ok, because the least common multiple of 1 and 2 or 2 and 2 is 2.