1. **Understanding the Problem:** We are given a pattern of relationships between pairs of letters. "CT" relates to "RQ" and "AI" relates to "DF". We need to find a similar relationship for "SP" among the options: MD, DN, AD, AI. 2. **Analyze the First Pair: CT and RQ** Let's look at the position of each letter in the alphabet (A=1, B=2, ..., Z=26): C=3, T=20 R=18, Q=17 Compare positions: From C to R: 3 to 18, difference = 18 - 3 = 15 From T to Q: 20 to 17, difference = 17 - 20 = -3 Check for a pattern: Sum of positions of CT: 3 + 20 = 23 Sum of positions of RQ: 18 + 17 = 35 Difference in sums = 35 - 23 = 12 3. **Analyze the Second Pair: AI and DF** A=1, I=9 D=4, F=6 From A to D: 1 to 4 = +3 From I to F: 9 to 6 = -3 Sum AI: 1 + 9 = 10 Sum DF: 4 + 6 = 10 4. **Observing the Pattern:** For the first pair: First letter increased by 15, second letter decreased by 3. Sum difference: +12 For second pair: First letter increased by 3, second letter decreased by 3. Sum difference: 0 The difference in the first letter's increment between pairs is 15 and 3. Second letter always decreased by 3. 5. **Check the Option that Matches the Pattern for SP:** S=19, P=16 Apply same increments from second pair (as AI->DF is simpler): First letter: 19 + 3 = 22 (V) Second letter: 16 - 3 = 13 (M) So SP would relate to VM if following the (AI->DF) pattern. Since VM is not an option, try first pair increments: First letter: 19 + 15 = 34 which exceeds 26, so wrap around: 34 - 26 = 8 (H) Second letter: 16 - 3 = 13 (M) So SP relates to HM. HM not in options. Try sum preservation like AI->DF (sum = 10) SP sum: 19 + 16 = 35 Check option sums: MD: M=13, D=4, sum=17 DN: D=4, N=14, sum=18 AD: A=1, D=4, sum=5 AI: A=1, I=9, sum=10 No option sums equal 35. 6. **Look for Letter Position Offsets Between Each Pair:** CT to RQ: C (3) to R (18): +15 T (20) to Q (17): -3 AI to DF: A (1) to D (4): +3 I (9) to F (6): -3 Notice that the second letter always shifts by -3. For the first letter, shifts are +15 and +3 respectively. It's possible the first letter shifts by multiples of 3, decreasing by 12 from first to second pair. If we apply first letter shift as +3 (like AI->DF), second letter shift as -3 to SP: S(19) + 3 = 22 (V) P(16) - 3 = 13 (M) VM is not an option. If we apply first letter shift as +15 (like CT->RQ), second letter shift as -3: S(19) + 15 = 34 - 26 = 8 (H) P(16) - 3 = 13 (M) HM not in options. 7. **Try the option that resembles AI (A I) and DF (D F) pattern:** Option d) AI is already a pair from example, unlikely. 8. **Try to check option b) DN:** D=4, N=14 If SP (19,16) relates to DN (4,14): First letter shift: 4 - 19 = -15 -> consistent with negative of 15 earlier Second letter shift: 14 - 16 = -2 (close to -3 from pattern) 9. **Conclusion:** Given the options, DN (option b) has first letter shift as -15, matching first pair but negative direction, and second letter shift close to -3. Thus, SP relates to DN by similar first letter shift magnitude and near second letter shift. **Final answer:** b) DN