i need math help asap

Question

At Bradley University, every math class has one and only one professor. Does this imply that there is a one to one correspondence between math classes and math professors? Be certain to give a full explanation.

Answer 1

_{No, there isn't necessarily a one-to-one correspondence between math classes and professors. If there were, then each math class must have one and only one professor AND each professor must teach one and only one math class. The second part isn't automatically true even if the first part is.}

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_{For example, say that Bradley University has only one math professor, who teaches multiple math classes. Then each of those classes has one and only one professor. However, that one professor is teaching more than one class, so there isn't a one-to-one correspondence between math classes and professors. }

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_{I hope that helps.}