how to use grep to filter out rows that contain dates that are before a certain day

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I have a sample employee data file, and I want to filter out the rows where the Employement_Status column is INACTIVE and the Hire_Date is before 2013 June 1st.

The rows in the file look like this

FirstName    LastName     BirthDate    EmploymentStatus    HireDate
  Tom           Red       5/16/1956        INACTIVE        4/13/1999
 Sandy         Green      12/21/1973       INACTIVE        12/20/2013
 John          Yellow     11/15/1983        ACTIVE         8/17/2000

And the grep command should only remove the second row.

Thank you very much

asked 24 secs ago

user59036

123

how to use grep to filter out rows that contain dates that are before a certain day