sorry - but I disagree with @MinhT1 's advise (yet the 2nd paragraph does use the word 'can' and not 'must')
You always have the option to claim or not claim a dependent; you CAN pick and choose!. The IRS doesn't care. There is no requirement that you MUST claim a dependent.
HOWEVER
your dependent does NOT have the same option. He must check the box that he CAN be claimed by someone else, whether or not that someone else (his parents in this case) claim him. So his answer is the same, regardless of his parent's action.
ps there is no such thing as 'claiming himself' for anyone. You can claim some one else (other than a spouse) given the IRS rules for claiming someone, but you do not claim yourself or your spouse.
