Solution Found!
a) Given a truth table, explain how to use disjunctive
Chapter 1, Problem 5RQ(choose chapter or problem)
Problem 5RQ
a) Given a truth table, explain how to use disjunctive normal form to construct a compound proposition with this truth table.
b) Explain why part (a) shows that the operators ∧, ∨, and ¬ are functionally complete.
c) Is there an operator such that the set containing just this operator is functionally complete?
Questions & Answers
QUESTION:
Problem 5RQ
a) Given a truth table, explain how to use disjunctive normal form to construct a compound proposition with this truth table.
b) Explain why part (a) shows that the operators ∧, ∨, and ¬ are functionally complete.
c) Is there an operator such that the set containing just this operator is functionally complete?
ANSWER:
Solution:
Step 1 :
In this problem we have to use disjunctive normal form to construct a compound proposition with this truth table.
A |
B |
C |
||||
T |
T |
T |
T |
T |
F |
F |
T |
T |
F |
T |
T |
F |
F |
T |
F |
T |
T |
T |
F |
F |
T |
F |
F |
T |
T |
F |
F |
F |
T |
T |
T |
T |
F |
F |
F |
T |
F |
T |
F |
T |
T |
F |
F |
T |
F |
T |
F |
T |
F |
F |
F |
F |
F |
T |
T |
.’. Disjunctive normal form is
Use the rows of the truth table where the proposition is true to construct minterms.
If the variable is true, use the propositional variable in the minterm.
If the variable is false, use the negation of the variable in the minterm.
Connect the minterms with us.