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Homework Statement
Construct a truth table to show:
Z=(A+(not)B).(B+C).((not)A+B+D)
Homework Equations
The Attempt at a Solution
from 0,0,0,0 to 1,1,1,1 i get
0,0,0,0,0,1,1,1,1,1,1,1,0,0,1,1
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A truth table is a table used in logic to show all possible combinations of inputs and their corresponding outputs for a logical expression. It is a helpful tool for evaluating the validity of logical statements.
To construct a truth table, you must first list all the variables or inputs for the logical expression. Then, you will create columns for each variable and an additional column for the output. Next, fill in the columns with all possible combinations of inputs and use the logical operators (such as AND, OR, NOT) to determine the output for each combination. Finally, label the output column with the logical expression and write "true" or "false" for each output.
The logical expression for Z=(A+(not)B).(B+C).((not)A+B+D) is simply Z. This is because the logical expression is already in its most simplified form, and Z represents the output of the expression.
This truth table will have 16 rows. This is because there are 4 variables (A, B, C, D) and each variable has 2 possible values (true or false), resulting in 2^4 = 16 possible combinations of inputs.
To determine the validity of a logical statement, you can look at the output column of the truth table. If the output is always true for every combination of inputs, then the statement is considered logically valid. If there is at least one combination of inputs that results in a false output, then the statement is considered invalid.