Decide whether the set A of positive integers divisible by 17 and B the set of positive integers
divisible by 11 are in bijection.

Explanation:

Two sets are in bijection if the function that relates them is bijective.

Thus, the question may be reformulated to: is it possible that the two sets A and B are related by a bijective function?

A bijective function is both inyective and surjective, which implies that it is invertible.

Inyective means that any element of the domain is mapped into exactly one element of the codomain.

Surjective means that each element of the codoman is related exactly with one element of the codomain.

That implies that there are no unpaired elements.

Assume the set A is the domain of your function and B is the codomain.

Then, the question is: is it possible for the set {17, 34, 51, 68, 85, . . .} to be in bijection with the set {11, 22, 33, 44, 55, . . . }?

Realize the two sets do not have common elements, because 17 and 34 are relative primes.

It is possible to set a bijective function of A onto B, or of B onto A, if and only if the two sets have the same cardinality (number of elements).

Indeed, the two sets A and B have the same cardinality: both have the same size, thus you may conclude that there could be a bijection relation between them and thus the two sets are in bijection.

The given two sets A and B are in the same cardiality and thereby in the bijection and this can be determined by using the given data.

GIven :

Set A : {17, 34, 51, 68, 85, . . .}

Set B : {11, 22, 33, 44, 55, . . .}

Bijection can be defined as the set of the injective and surjective variables. The set has been termed be injective and surjective when there has been the absence of the unpaired elements in the sets.

The given set has been of 17, 34 …. and another set has been 11, 22… The two sets have been consisted of the common element and thereby the common cardiality. Thus, the two sets have been in the bijection with one another.

For more information about the bijection, refer to the link given below:

link

m∠a is 90°

m∠b is 40°