Question
The logical operators NAND (not and) and NOR (not or) are defined as follows:$$\begin{aligned} p \mathrm{NAND} q &=\sim(p \wedge q) \\ p \mathrm{NOR} q &=\sim(p \vee q) \end{aligned}$$Construct a truth table for each proposition.$$p \text { NOR } q$$
Step 1
The NOR operator is defined as the negation of the OR operator. In other words, if either p or q is true, then p NOR q is false. If both p and q are false, then p NOR q is true. Show more…
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The logical operators NAND (not and) and NOR (not or) are defined as follows: $$\begin{aligned} p \mathrm{NAND} q &=\sim(p \wedge q) \\ p \mathrm{NOR} q &=\sim(p \vee q) \end{aligned}$$ Construct a truth table for each proposition. $$ p \text { NAND } q $$
The Language Of Logic
Logical Equivalences
The following exercises involve the logical operators $N A N D$ and $N O R$. The proposition $p$ NAND $q$ is true when either $p$ or $q$, or both, are false; and it is false when both $p$ and $q$ are true. The proposition $p$ NOR $q$ is true when both $p$ and $q$ are false, and it is false otherwise. The propositions $p$ NAND $q$ and $p$ NOR $q$ are denoted by $p \mid q$ and $p \downarrow q$, respectively. (The operators | and $\downarrow$ are called the Sheffer stroke and the Peirce arrow after H. M. Sheffer and C. S. Peirce, respectively.) Construct a truth table for the logical operator $\mathrm{NOR}$.
The Foundations: Logic and Proofs
Propositional Equivalences
The following exercises involve the logical operators $N A N D$ and $N O R$. The proposition $p$ NAND $q$ is true when either $p$ or $q$, or both, are false; and it is false when both $p$ and $q$ are true. The proposition $p$ NOR $q$ is true when both $p$ and $q$ are false, and it is false otherwise. The propositions $p$ NAND $q$ and $p$ NOR $q$ are denoted by $p \mid q$ and $p \downarrow q$, respectively. (The operators | and $\downarrow$ are called the Sheffer stroke and the Peirce arrow after H. M. Sheffer and C. S. Peirce, respectively.) Construct a truth table for the logical operator $N A N D$.
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