Step 1: Understanding the Concept:
Double-stranded DNA molecules conform to Chargaff's rules of base pairing.
These rules state that the total amount of adenine (\( A \)) is equal to thymine (\( T \)), and the total amount of cytosine (\( C \)) is equal to guanine (\( G \)).
Therefore, we have the equalities:
\[ A = T \quad \text{and} \quad G = C \]
From these base equalities, various ratios and algebraic equations can be verified.
Step 2: Detailed Explanation:
Let us analyze each mathematical statement using the base identities \( A = T \) and \( G = C \).
- Statement (A) \( A + T = G + C \): This is incorrect because the ratio of \( (A + T) / (G + C) \) varies significantly across different organisms and is rarely equal to 1.
- Statement (B) \( A = G; C = T \): This is incorrect because adenine does not pair with guanine, and cytosine does not pair with thymine. Their concentrations are independent.
- Statement (C) \( A/T = C/G \): Since \( A = T \implies A/T = 1 \), and \( C = G \implies C/G = 1 \), we have \( 1 = 1 \). This statement is correct.
- Statement (D) \( T/A = C/G \): Similarly, since \( T = A \implies T/A = 1 \), and \( C = G \implies C/G = 1 \), we have \( 1 = 1 \). This statement is correct.
- Statement (E) \( A + G = C + T \): This represents the equality of total purines (\( A + G \)) and total pyrimidines (\( C + T \)). Since \( A = T \) and \( G = C \), their sums must be equal. This statement is correct.
Therefore, only statements (C), (D), and (E) are structurally valid for double-stranded DNA.
Step 3: Final Answer:
The correct statements are (C), (D), and (E), corresponding to option 4.