The doctrine applies in Canada ,where there is a federal law

A noun becomes a compound noun when it combines with another noun using the conjunction ‘and’ and is plural in number per se.

For example: There is a brother and a sister in this class, is wrong because, a sister and a brother put together becomes a compound and plural noun entailing a plural verb. The correct version is ‘There are a sister and a brother in this class.’ Hence You can dump A and D.
B is the correct one; here ‘that’ is the subject of the subordinate clause; ‘that’ stands for both the laws and the word ‘each’ indicates that the laws individually and jointly are valid and consistent.

C is wrong because of using the unidiomatic ‘both of which are each’. Each is an unnecessary intrusion

E is wrong becos of saying that the laws are each valid ‘or’ consistent. Valid ‘or’ consistent distorts the intended meaning of the original passage.

it becomes plural verb as two nouns are combined using the conjunction '‘and’' .

[quote="Praetorian"]The doctrine applies in Canada ,where there is a federal law and a provincial law that are each valid and consistent.

a. is a federal law and a provincial law that are each valid and
b.are a federal law and a provincial law that are each valid and
c.are a federal law and a provincial law both of which are each valid and
d. is a federal law and a provincial law both of which are each valid and
e.are a federal law and a provincial law that are each valid or

IMO, B is the answer