## Discrete Mathematics with Applications 4th Edition

$1$
The lower limit of $j$ is $0$ and the upper limit is also $4$. Thus, evaluate the given products from $j=0$ to $j=4$ to obtain: $=(-1)^0 \cdot (-1) \cdot (-1)^2 \cdot (-1)^3 \cdot (-1)^4 \\=1 \cdot (-1) \cdot 1 \cdot (-1) \cdot 1$ Multiply two factors at a time to obtain: $\\=-1 \cdot 1 \cdot (-1) \cdot 1 \\=-1 \cdot (-1) \cdot 1 \\=1 \cdot 1 \\=1$