Then these nodes communicate with its peers to check the validity of transaction on the mempool.
They communicate to exchange unconfirmed transactions. Not to check / question its validity. That happens locally, and is done by each node individually.
Thank you for the clarification I stand corrected, yeah they exchanges unconfirmed transaction, no excuses I messed up there

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I messed up this line
Each Bitcoin node has its own mempool, where it stores the queue of transactions that it has checked and considers valid.
In addition we can also see the difference of mempool and blockchain function in this quotation.
The memory pool holds fresh or unconfirmed transactions (stored as individual transactions).
The blockchain holds archived or confirmed transactions (packaged in blocks).