Sorry to tell you That is the worst possible thing to do and it will be useless as 5 min later they will forget what you said anyway. You are only setting yourself up with a lot of needless agitation and even aggression.
The sooner everyone plays along by saying ‘oh really that’s interesting’ or ‘ did that really happen?’ ‘That’s nice’ the happier you’ll all be.
I’d say this is the very first and most important lesson I learnt.
You can actually have fun and get a lot of laughs when not so uptight about the ‘truth’.
Relax and accept their ‘truth’ is probably remembered from many years ago or as they lose sense of time and space, they just lose thoughts altogether.
Really what harm is it if they think they went to the shops yesterday when they actually stayed home?
Being mindful not to cause conflict (and continually righting a person will cause conflict) and frustration, will go a long way for a more peaceful household. Hope this helps.

No! no! No! You will never be able to get them to understand and it’s torture for them and frustrating for you! I’ll say again look up Teepa snow on you tube she addresses many issues

Trying to explain only makes matters worse. I find it's best to agree and change the subject.

You cannot reason with a dementia patient. Brain cells are dead and dying. So you can explain until the cows come home, but he/she cannot "get it!" Even if he says he understands, he probably doesn't and he will forget it anyway. So many people including relatives have no clue about the diseases!

It is best to go along with them and not try to correct them. It is hard for me to do that but it's the best thing for them.