Questions: Let A=0,1,2 and B=5,6,7. Let R be the relation from A to B such that (a, b) in R provided that a+b=6. Then all the pairs in R are (0,6),(1,5)(6,0),(5,1). True False

Solution Steps

To determine if the given statement about the relation \( R \) is true or false, we need to find all pairs \((a, b)\) such that \(a \in A\), \(b \in B\), and \(a + b = 6\). We will then compare these pairs with the ones provided in the statement.

Let \( A = \{0, 1, 2\} \) and \( B = \{5, 6, 7\} \). The relation \( R \) consists of pairs \( (a, b) \) such that \( a \in A \), \( b \in B \), and \( a + b = 6 \).

We will find all pairs \( (a, b) \) that satisfy the equation \( a + b = 6 \):

• For \( a = 0 \): \( b = 6 \) (valid pair: \( (0, 6) \))
• For \( a = 1 \): \( b = 5 \) (valid pair: \( (1, 5) \))
• For \( a = 2 \): \( b = 4 \) (not in \( B \))

Thus, the valid pairs in \( R \) are \( \{(0, 6), (1, 5)\} \).

The given pairs in the statement are \( \{(0, 6), (6, 0), (5, 1), (1, 5)\} \). We compare these with the valid pairs found:

• Valid pairs: \( \{(0, 6), (1, 5)\} \)
• Given pairs: \( \{(0, 6), (6, 0), (5, 1), (1, 5)\} \)

The pairs \( (6, 0) \) and \( (5, 1) \) are not valid since \( 6 \notin A \) and \( 5 \notin B \).

Final Answer