Question

Select all that apply For which of these scenarios is it impossible for a function from a set A to a set B to be one-to-one?

a.∣A∣=10,∣B∣=11
b.∣A∣=11,∣B∣=10
c.∣A∣=1,∣B∣=1
d.∣A∣=∣B∣=10
e.∣A∣=2,∣B∣=1

Answer 1

It is impossible for a function from set A to set B to be one-to-one if the number of elements in A is greater than the number of elements in B. Therefore, scenarios b (|A|=11, |B|=10) and e (|A|=2, |B|=1) are impossible for a one-to-one function.

Step-by-step explanation:

The student has asked which scenarios make it impossible for a function from a set A to a set B to be one-to-one. A one-to-one function, also known as an injective function, means that for every element in the domain (set A) there is a unique element in the codomain (set B).

This implies that the size of set A cannot exceed the size of set B, otherwise there would not be enough unique elements in set B to accommodate a one-to-one correspondence.

• b. |A| = 11, |B| = 10
• e. |A| = 2, |B| = 1

In scenario b, the set A has more elements than set B, making it impossible for each element in A to be matched with a unique element in B. In scenario e, there are again more elements in A than in B, which also prevents the possibility of a one-to-one function.

The other scenarios listed a, c, and d have an equal or greater number of elements in set B compared to set A, and so a one-to-one function could be possible.