Bernard retired after $35$ years as a teacher in Newcastle, California, and moved to Washington because they do not levy income taxes. He retired in June and moved into his new home in Washington on September $12,2023.$ He started receiving a $$3,000$ monthly pension from the State Teachers Retirement System in July $($monthly payments on the last day of the month$).$ Which of the following statements is correct?

He must pay tax to California on $$18,000$ of pension income.

Because he was a Washington resident at the end of the year, he does not need to pay any tax on the pension income to California.

He must pay tax to California on the $$6,000$ of pension income he received in July and August. However, he will not pay California tax on the $$12,000$ pension income he received after he became a Washington resident.

He must pay tax on $75\%($$$13,500)$ of the pension income because he resided in California for eight full months during the year.