Which sentence does not show correct pronoun agreement?

1. either patricia or janet left her music on the piano.
2. either patricia or janet left their music on the piano.
3. both patricia and janet left their music on the piano.

2). Either Patricia or Janet left their music on the piano.

Explanation:

Pronoun antecedent agreement asserts that the pronoun and its antecedent used in the sentence must agree in number.

As per the question, option 2 displays the sentence that does not show a correct pronoun agreement as the sentence involves two antecedents 'Patricia' and 'Janet' and the closer of them would be referred. According to this rule, the correct antecedent would be 'her' instead of 'their'(to denote 'Janet' and agree with the closest pronoun in number). The other options correctly employs the pronoun agreement as option 1 follows the above rule while option 3 uses the correlative conjunction 'both..also' which comes up with a plural antecedent as it denotes more than one pronoun. Thus, option 2 is the correct answer.