The Employees' Provident Funds and Miscellaneous Provisions Act, 1952, stipulates certain exemptions about the applicability of its provisions to cooperative societies. The question specifically asks about establishments registered under the Co-operative Societies Act, 1912, to which this act does not apply.

1. The key part of the question is to identify the conditions under which a cooperative society establishment is exempt from the Act. According to the act, one of the main criteria for exemption is that it applies to establishments that operate without the aid of power and employ fewer than 50 persons.
2. Let's analyze the provided options:
   • Option 1: Establishments employing fewer than 50 persons and operating without the aid of power. This matches the criteria given for exemption by the Act, thus this option is the correct answer.
   • Option 2: Establishments employing fewer than 70 persons and operating with the aid of power. This does not meet the criteria as it involves the use of power.
   • Option 3: Establishments employing more than 50 persons or operating without the aid of power. This option does not meet the exemption criteria because employing more than 50 persons does not qualify for an exemption.
   • Option 4: Establishments employing fewer than 20 persons or operating without the aid of power. While this option mentions operating without the aid of power, the condition about the number of employees is not a standard criterion mentioned for this exemption.
3. Thus, the correct answer is Establishments employing fewer than 50 persons and operating without the aid of power.

Therefore, the Employees' Provident Funds and Miscellaneous Provisions Act, 1952, does not apply to cooperative society establishments that fulfill this criteria.