.A logic operator not defined in this chapter is the NAND function; it is denoted by ↑. NAND is short for “not AND” where a ↑ b ≡ ~ (a ∧ b). a. Give the truth table for the two-input NAND function b.Show that the NAND operator can be used to simulate each of the AND, OR, and NOT operators.
2 .A logic operator not defined in this chapter is the NAND function; it is denoted by ↑. NAND is short for “not AND” where a ↑ b ≡ ~ (a ∧ b).
a. Give the truth table for the two-input NAND function
b.Show that the NAND operator can be used to simulate each of the AND, OR, and NOT operators.
In chapter 5, you have learned about De Morgan’s Law. You have also learned how to prove the validity of propositional logic arguments. Please refer to section 5.2.3 of your book to learn more about these concepts.
To answer the second part of the questions, you should know well about the above laws and logics and you need to know how and where to apply De Morgan’s Law, implication, conjunction, double negation and so on….
To show that NAND is equivalent to not, you have to pick a variable and show that a NAND “a” equals “not a” (just by Applying bullion logic). Note that the not operator is a unary operator (it operates only on a single variable).
a NAND a = !a or in another form we can show a ↑ a = ~ a
Now if we want to show that NAND is equivalent to OR operator, we should show the following using double negation, De Morgan’s law and implication.
And you need to do almost the same to show that NAND is equivalent to AND operator.
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