Which of the following statement is false?

The public Ethereum blockchain is run by the Ethereum foundation, while private or consortium blockchains can be run by any organization that chooses to set them up$.$

The public Ethereum blockchain uses the cryptocurrency Ether as the native token, while private or consortium blockchains use Bitcoin and Zcash, repectively.

It is possible for anyone to participate in using the public Ethereum blockchain. Private or consortium blockchains can place restrictions on who is able to join and participate in their networks.

The public Ethereum blockchain uses proof$-$of$-$work as the consensus mechanism, while a private or consortium blockchain can choose that or a different consensus mechanism to agree on new blocks.