Answer :
To determine which formulas correctly represent adding \( A_1 \) and \( B_1 \) and then subtracting \( C_1 \), let's analyze each option in detail.
Option A:
[tex]\[ C_1 - A_1 + B_1 \][/tex]
This formula does not follow the required sequence. First, it subtracts \( A_1 \) from \( C_1 \) and then adds \( B_1 \). This isn't equivalent to adding \( A_1 \) and \( B_1 \) first and then subtracting \( C_1 \).
Option B:
[tex]\[ A_1 + B_1 - C_1 \][/tex]
This formula adds \( A_1 \) and \( B_1 \) together and then subtracts \( C_1 \). This matches the requirement perfectly.
Option C:
[tex]\[ (A_1 + B_1) - C_1 \][/tex]
This is a rephrased version of option B, where the parentheses indicate that \( A_1 \) and \( B_1 \) are added first and then \( C_1 \) is subtracted. This also matches the requirement perfectly.
Option D:
[tex]\[ A_1 + B_1 - C_1 \][/tex]
This formula is the same as Option B, adding \( A_1 \) and \( B_1 \) first, and then subtracting \( C_1 \), which again matches the requirement perfectly.
Thus, the formulas that apply are:
1. Option B: \( A_1 + B_1 - C_1 \)
2. Option C: \( (A_1 + B_1) - C_1 \)
3. Option D: \( A_1 + B_1 - C_1 \)
Hence, the two selected options that correctly follow the given instruction are Option B and Option C.
Option A:
[tex]\[ C_1 - A_1 + B_1 \][/tex]
This formula does not follow the required sequence. First, it subtracts \( A_1 \) from \( C_1 \) and then adds \( B_1 \). This isn't equivalent to adding \( A_1 \) and \( B_1 \) first and then subtracting \( C_1 \).
Option B:
[tex]\[ A_1 + B_1 - C_1 \][/tex]
This formula adds \( A_1 \) and \( B_1 \) together and then subtracts \( C_1 \). This matches the requirement perfectly.
Option C:
[tex]\[ (A_1 + B_1) - C_1 \][/tex]
This is a rephrased version of option B, where the parentheses indicate that \( A_1 \) and \( B_1 \) are added first and then \( C_1 \) is subtracted. This also matches the requirement perfectly.
Option D:
[tex]\[ A_1 + B_1 - C_1 \][/tex]
This formula is the same as Option B, adding \( A_1 \) and \( B_1 \) first, and then subtracting \( C_1 \), which again matches the requirement perfectly.
Thus, the formulas that apply are:
1. Option B: \( A_1 + B_1 - C_1 \)
2. Option C: \( (A_1 + B_1) - C_1 \)
3. Option D: \( A_1 + B_1 - C_1 \)
Hence, the two selected options that correctly follow the given instruction are Option B and Option C.
