How can confidentiality and authentication be achieved using public key cryptography?

What will be an ideal response?

If confidentiality is a major concern for User A, she encrypts the message with the recipient's public key. That way, only the recipient can decrypt the message with his private key. If User A wants to assure User B that she is indeed the person sending the message (authentication), she can encrypt the message with her private key. After all, she's the only person who possesses her private key.