The question asks to identify the correct relationships between different lung volume measurements. We need to evaluate each statement based on standard respiratory physiology definitions.

Option 1 Analysis: Vital Capacity minus Expiratory Reserve Volume

Statement: Vital capacity minus expiratory reserve volume equals inspiratory capacity.

• Definitions:
  • Vital Capacity ($\text{VC}$): Maximum volume of air that can be exhaled after a maximal inhalation. $\text{VC} = \text{Tidal Volume (TV)} + \text{Inspiratory Reserve Volume (IRV)} + \text{Expiratory Reserve Volume (ERV)}$.
  • Inspiratory Capacity ($\text{IC}$): Maximum volume of air that can be inhaled after a normal tidal exhalation. $\text{IC} = \text{TV} + \text{IRV}$.
  • Expiratory Reserve Volume ($\text{ERV}$): Maximum volume of air that can be forcefully exhaled after a normal tidal exhalation.
• Relationship Check: If we subtract $\text{ERV}$ from $\text{VC}$, we get: $ \text{VC} - \text{ERV} = (\text{TV} + \text{IRV} + \text{ERV}) - \text{ERV} $ $ \text{VC} - \text{ERV} = \text{TV} + \text{IRV} $ Since $\text{IC} = \text{TV} + \text{IRV}$, it follows that $\text{VC} - \text{ERV} = \text{IC}$.
• Conclusion: This statement is CORRECT.

Option 2 Analysis: Vital Capacity plus Expiratory Reserve Volume

Statement: Vital capacity plus expiratory reserve volume equals inspiratory capacity.

• Relationship Check: Based on the definitions above, $\text{VC} = \text{IC} + \text{ERV}$. Adding $\text{ERV}$ to $\text{VC}$ would result in a volume larger than $\text{IC}$. The statement $\text{VC} + \text{ERV} = \text{IC}$ is incorrect.
• Conclusion: This statement is INCORRECT.

Option 3 Analysis: Total Lung Capacity sum

Statement: Total lung capacity equals the sum of inspiratory capacity and functional residual capacity.

• Definitions:
  • Total Lung Capacity ($\text{TLC}$): Total volume of air in the lungs after maximal inhalation. $\text{TLC} = \text{VC} + \text{Residual Volume (RV)}$.
  • Functional Residual Capacity ($\text{FRC}$): Volume of air remaining in the lungs after normal tidal exhalation. $\text{FRC} = \text{ERV} + \text{RV}$.
  • Inspiratory Capacity ($\text{IC}$) = $\text{TV} + \text{IRV}$.
• Relationship Check: Let's sum $\text{IC}$ and $\text{FRC}$: $ \text{IC} + \text{FRC} = (\text{TV} + \text{IRV}) + (\text{ERV} + \text{RV}) $ $ \text{IC} + \text{FRC} = \text{TV} + \text{IRV} + \text{ERV} + \text{RV} $ We know that $\text{TLC} = \text{VC} + \text{RV} = (\text{TV} + \text{IRV} + \text{ERV}) + \text{RV}$. Therefore, $\text{IC} + \text{FRC}$ is indeed equal to $\text{TLC}$.
• Conclusion: This statement is CORRECT.

Option 4 Analysis: Functional Residual Capacity difference

Statement: Functional residual capacity is the difference of expiratory reserve volume and residual volume.

• Relationship Check: The standard definition is $\text{FRC} = \text{ERV} + \text{RV}$. The statement proposes $\text{FRC} = \text{ERV} - \text{RV}$.
• Conclusion: This statement is INCORRECT.

Summary of Correct Relations

Based on the analysis, the following relations are correct:

• Option 1: $\text{VC} - \text{ERV} = \text{IC}$
• Option 3: $\text{TLC} = \text{IC} + \text{FRC}$

The correct options are 1 and 3.