Question

QI.

List the ordered pairs in the relation R from A = (0,1,2,3,4) to B = [0,1,2,3), where
(a,b) ER if and only if Icm(a, b) = 2.​

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.