This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Construct the multiplication table for modulo 8 on the set \1, 3, 5, 7\. The operation is a b = (a × b) 8. |c|c|c|c|c| & 1 & 3 & 5 & 7 \\ 1 & 1 & 3 & 5 & 7 \\ 3 & 3 & 1 & 7 & 5 \\ 5 & 5 & 7 & 1 & 3 \\ 7 & 7 & 5 & 3 & 1 \\ Step 2: Evaluate (5 3) 7. First, find 5 3 from the table. 5 3 = 7 Next, evaluate 7 7. 7 7 = 1 So, (5 3) 7 = 1. Step 3: Find the truth set of m (m+2) = 3. We test each value of m from the set \1, 3, 5, 7\. Remember that (m+2) is also evaluated modulo 8. • For m=1: m+2 = 1+2 = 3. 1 3 = 3. This matches the equation. • For m=3: m+2 = 3+2 = 5. 3 5 = 7. This does not match 3. • For m=5: m+2 = 5+2 = 7. 5 7 = 3. This matches the equation. • For m=7: m+2 = 7+2 = 9. 9 8 = 1. So we evaluate 7 1. 7 1 = 7. This does not match 3. The values of m that satisfy the equation are 1 and 5. The truth set is \1, 5\. That's 2 down. 3 left today — send the next one.