Should I be honest on my LinkedIn (See Post)

I recently started a job a month ago, my boss was hired at the same time. Recently my boss got fired for not updating his LinkedIn.

I’m taking this as a red flag and I’m looking for a new job.

Since I only worked at this job for a month, should I leave my LinkedIn as is? Showing I only worked there for a month?

I have a big gap on my LinkedIn as I was laid off in October. I did work another job for 3 months before this, but I don’t want to show myself quitting jobs right away.

Should I be honest on my linked in?