There are distinct differences between Flexible Spending Accounts $($FSAs$)$ and Health Savings Accounts $($HSAs$).$ Identify the false statement below.

Both contributions to FSAs and HSAs are tax$-$deductible and lower the taxpayer$$s taxable income.

FSAs are set up and owned by the employer and can be lost through job changes.

Both FSAs and HSAs are used to save money on a pre$-$tax basis to be used for future medical expenses and do not expire.

HSAs have higher contribution limits than FSAs, as well as the $$1,000$ catch$-$up contribution for taxpayers over age$55.$