In Professional Air Traffic Controllers (PATCO) Org. v. Fair Labor Relations Authority, PATCO and the Federal Aviation A

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In Professional Air Traffic Controllers (PATCO) Org. v. Fair
Labor Relations Authority, PATCO and the Federal Aviation Authority
(FAA) held a negotiation for a new agreement which was rejected by
PATCO. Following the rejection, the parties resumed negotiation
again, but when the negotiation failed to reach an agreement, PATCO
went on strike against FAA. Is it illegal for PATCO to engage in a
strike?
No, it is not illegal for PATCO to strike as the federal
employees have constitutional right to strike.
Yes, it is illegal for PATCO to strike as it is a federal
organization and federal employees are forbidden to strike.
No, it is not illegal for PATCO to strike because PATCO had been
granted special permission to strike through court order.
Yes, PATCO being an exclusive collective bargaining
representative has the right to strike.