If \(a \in \{-1,2,3,4,5\}\) and \(b \in \{0,3,6\}\), Write the Set of All Ordered Pairs \((a,b)\) Such That \(a+b=5\)
Question
If \[ a \in \{-1,2,3,4,5\} \] and \[ b \in \{0,3,6\}, \] write the set of all ordered pairs \((a,b)\) such that \[ a+b=5. \]
Solution
Given:
\[ A=\{-1,2,3,4,5\} \]
\[ B=\{0,3,6\} \]
We find the ordered pairs satisfying:
\[ a+b=5 \]
For \(a=-1\),
\[ -1+b=5 \]
\[ b=6 \]
So, ordered pair is:
\[ (-1,6) \]
For \(a=2\),
\[ 2+b=5 \]
\[ b=3 \]
So, ordered pair is:
\[ (2,3) \]
For \(a=3\),
\[ 3+b=5 \]
\[ b=2 \]
But \(2 \notin B\), so no ordered pair.
For \(a=4\),
\[ 4+b=5 \]
\[ b=1 \]
But \(1 \notin B\), so no ordered pair.
For \(a=5\),
\[ 5+b=5 \]
\[ b=0 \]
So, ordered pair is:
\[ (5,0) \]
Therefore,
\[ \boxed{\{(-1,6),\ (2,3),\ (5,0)\}} \]