code: def test_setops_preserve_freq(self, tz):
      rng = date_range("1/1/2000", "1/1/2002", name="idx", tz=tz)
  
      result = rng[:50].union(rng[50:100])
      assert result.name == rng.name
      assert result.freq == rng.freq
      assert result.tz == rng.tz
  
      result = rng[:50].union(rng[30:100])
      assert result.name == rng.name
      assert result.freq == rng.freq
      assert result.tz == rng.tz
  
      result = rng[:50].union(rng[60:100])
      assert result.name == rng.name
      assert result.freq is None
      assert result.tz == rng.tz
  
      result = rng[:50].intersection(rng[25:75])
      assert result.name == rng.name
      assert result.freqstr == "D"
      assert result.tz == rng.tz
  
      nofreq = DatetimeIndex(list(rng[25:75]), name="other")
      result = rng[:50].union(nofreq)
      assert result.name is None
      assert result.freq == rng.freq
      assert result.tz == rng.tz
  
      result = rng[:50].intersection(nofreq)
      assert result.name is None
      assert result.freq == rng.freq
      assert result.tz == rng.tz
  
imports: from datetime import datetime, timezone
  import numpy
  import pytest
  import pytz
  import pandas.util._test_decorators
  import pandas
  from pandas import DataFrame, DatetimeIndex, Index, Series, Timestamp, bdate_range, date_range
  import pandas._testing
  from pandas.tseries.offsets import BMonthEnd, Minute, MonthEnd
label_desc: Use image node_id 20 for calling the TestDatetimeIndexSetOps obj's underlying member method code with example usage: obj.test_setops_preserve_freq(tz) without return types