# Thread: class of equivalence

1. ## class of equivalence

hello! i need help

Suppose that R is a relation on the set of positive integers such that:
aRb if and only if l(a) = l(b)

where l(x) is the number of decimal digits of x. (for example l(122) is 3)

we already proved that R is an equivalence relation..the question is:

Considers the set of numbers formed from the 4 digits 1, 2, 3 and 4.
What is the equivalence class of 12?

thank you

2. Originally Posted by qwerty321
hello! i need help

Suppose that R is a relation on the set of positive integers such that:
aRb if and only if l(a) = l(b)

where l(x) is the number of decimal digits of x. (for example l(122) is 3)

we already proved that R is an equivalence relation..the question is:

Considers the set of numbers formed from the 4 digits 1, 2, 3 and 4.
What is the equivalence class of 12?

thank you
It is the set of all 2 digit numbers with digits selected from {1,2,3,4}

CB

3. There are a total of $2^4= 16$ two digit numbers in that set.

Here are four of them: 11, 12, 13, 14.
Can you find the other twelve?