Question:
Let \( +_6 \) be addition modulo 6 on the set \( S = \{0,1,2,3,4,5\} \). Evaluate:
\[ 2 +_6 4^{-1} +_6 3^{-1} \]
Concept:
In addition modulo \(6\), the inverse of \(a\) is:
\[ a^{-1} = 6 – a \]
—Solution:
Step 1: Find inverses
- \(4^{-1} = 6 – 4 = 2\)
- \(3^{-1} = 6 – 3 = 3\)
Step 2: Substitute
\[ 2 +_6 2 +_6 3 \]
Step 3: Add modulo 6
\[ 2 + 2 + 3 = 7 \equiv 1 \pmod{6} \]
Final Answer:
\[ \boxed{1} \]