Final answer:
To show that xz = (x+y)(x+y’)(x’+z), you can either use a truth table or Boolean identities. In the truth table method, assign values of 0 and 1 to x, y, y’, and z, and calculate the values for each column. Check if the left-hand side (xz) is equal to the right-hand side ((x+y)(x+y’)(x’+z)) for all rows. In the Boolean identities method, apply the distributive law and simplify the expression using Boolean identities until it becomes xz.
Step-by-step explanation:
To show that xz = (x+y)(x+y’)(x’+z) using a truth table, you can create a truth table with columns for x, y, y’, z, (x+y), (x+y’), and (x’+z). Assign values of 0 and 1 to x, y, y’, and z, and calculate the values for each column. Then, check if the left-hand side (xz) is equal to the right-hand side ((x+y)(x+y’)(x’+z)) for all rows. If they are equal for all rows, then the statement is true. To show it using Boolean identities, you can rewrite the expression using the distributive law and complement law. Start with the expression (x+y)(x+y’)(x’+z), apply the distributive law, and simplify the expression using Boolean identities until it becomes xz.