1) The operation \( \nabla \) is defined on the set R of eal numbers by \( m \nabla n=m+n+l o \) Evaluatej a. \( 3 \nabla(4+5) \) \( b_{1}(3 \nabla 4)+(3 \nabla 5) \)

To evaluate the operation \( m \nabla n = m + n + l o \), we first need to clarify what \( l o \) represents. Since it is not defined in your question, I will assume it is a constant value. For the sake of this evaluation, let's denote \( l o \) as \( c \), where \( c \) is some constant. Now, we can rewrite the operation as: \[ m \nabla n = m + n + c \] ### a. Evaluate \( 3 \nabla (4 + 5) \) First, calculate \( 4 + 5 \): \[ 4 + 5 = 9 \] Now, substitute this into the operation: \[ 3 \nabla 9 = 3 + 9 + c = 12 + c \] ### b. Evaluate \( (3 \nabla 4) + (3 \nabla 5) \) First, calculate \( 3 \nabla 4 \): \[ 3 \nabla 4 = 3 + 4 + c = 7 + c \] Next, calculate \( 3 \nabla 5 \): \[ 3 \nabla 5 = 3 + 5 + c = 8 + c \] Now, add the two results: \[ (3 \nabla 4) + (3 \nabla 5) = (7 + c) + (8 + c) = 15 + 2c \] ### Summary of Results - a. \( 3 \nabla (4 + 5) = 12 + c \) - b. \( (3 \nabla 4) + (3 \nabla 5) = 15 + 2c \) If you have a specific value for \( c \), you can substitute it in to get numerical results.