Here is what I understand, the step to PoW are:
step 1:Miner select some transactions from its mempool.
step 2:Miner tries to create a block and then broadcasts it if successful.
step 3:Other miners check if the hash of the block with the nonce results in the required hash of the block sent from the previous miner.
step 4:Once other miners verify it is added to the block chain.
What if the miner add a false transaction to a block and then create a nonce for that block. I know that it will be ignored and detected as spam. But how will other miners know that the particular block has an invalid transaction, since other miners only verify the nonce and the hash?