Which of the following CNF expressions are satisfiable? If the expression is satisfiable, then give an assignment to the variables that causes the expression to evaluate to 1. If the expression is not satisfiable, then give the input/output table showing that no assignment to the variables satisfies the expression. (a) (x+z)(x+y)(y+z) Solution Satisfiable: the assignment x=1,y=z=0 is a satisfying assignment. The assignment x=0,y=z=1 is also a satisfying assignment. (b) (x+z)(x+y)(y+z)(x+y+z).

1. Which of the following CNF expressions are satisfiable? If the expression is satisfiable, then
give an assignment to the variables that causes the expression to evaluate to 1. If the expression
is not satisfiable, then give the input/output table showing that no assignment to the variables
satisfies the expression. (a) (x+z)(x+y)(y+z)
Solution
Satisfiable: the assignment x=1,y=z=0 is a satisfying assignment. The assignment x=0,y=z=1 is
also a satisfying assignment. (b) (x+z)(x+y)(y+z)(x+y+z)