Comment: We ARE NOT talking about a group of parents, one for each child.

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In reply to comment: You should since your the one (see in situ)

We ARE NOT talking about a group of parents, one for each child.

There is no plurality of children being considered.

We are only dealing with the parent(s) of any ONE child at a time.

Any notion otherwise, as you are trying to espouse, is completely nonsensical to the subject at hand.