Final answer:
After examining all the Boolean expressions provided, assuming that '2' is a typo for 'z', all expressions are satisfiable as there is at least one set of variable assignments that makes each expression true. There is no option that is not satisfiable among the ones given.
Step-by-step explanation:
The student has asked to select the Boolean expression that is not satisfiable from the given options. A satisfiable Boolean expression is one where there is at least one set of variable assignments that makes the expression true. Analyzing the provided expressions:
- (xy)(x + z)(y+z)
- (x + y) (x + 2)(y+z)
- (x+y)(x + 2) (y+z)
- (x + y) (x + 2) (y+z)
Here, '2' is not a Boolean variable but may be a typo for 'z'. However, if we treat '2' as 'z', then options (b), (c), and (d) are the same, meaning that none of these options could be considered unsatisfiable as they would be valid under the same conditions. Option (a) is also satisfiable for various assignments of x, y, and z, such as when all variables are true and hence the expression is true. Given the information provided and assuming the repeated options are typos, all of the expressions provided are satisfiable. Therefore, as per the instructions, we ignore any typos and irrelevant parts of the questions, and it appears that all options are actually satisfiable under the correct assignments.