Questions: What are the two equivalent translations of a "neither...nor" statement? ¬p ∧ ¬q ¬(p ∨ q)

What are the two equivalent translations of a "neither...nor" statement? ¬p ∧ ¬q ¬(p ∨ q)
Transcript text: What are the two equivalent translations of a "neither...nor" statement? $\neg p \wedge \neg q$ $\neg(p \vee q)$
failed

Solution

failed
failed

Solution Steps

Step 1: Understanding the "Neither...Nor" Statement

A "neither...nor" statement is a logical expression that negates both components of a compound statement. In logical terms, "neither \( p \) nor \( q \)" can be expressed as \(\neg p \wedge \neg q\), which means "not \( p \) and not \( q \)".

Step 2: Identifying Equivalent Translations

The logical expression \(\neg p \wedge \neg q\) can be equivalently expressed using De Morgan's laws. According to De Morgan's laws, the negation of a disjunction is equivalent to the conjunction of the negations:

\[ \neg(p \vee q) \equiv \neg p \wedge \neg q \]

Thus, the two equivalent translations of a "neither...nor" statement are:

  1. \(\neg p \wedge \neg q\)
  2. \(\neg(p \vee q)\)
Step 3: Selecting the Correct Options

From the given options, the two equivalent translations of a "neither...nor" statement are:

  • \(\neg p \wedge \neg q\)
  • \(\neg(p \vee q)\)

Final Answer

\[ \boxed{\neg p \wedge \neg q, \neg(p \vee q)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
In which way does the use of the signing statements by presidents differ from the use of the executive orders? Executive orders usually create new policies, where signing statements alter a policy already passed by Congress. Executive orders require the consent of Congress and signing statements do not. There is no difference between signing statements and executive orders. Presidents can issue only a limited number of executive orders but can issue unlimited signing statements.
failedAnswered
In the laboratory a student finds that it takes 129 Joules to increase the temperature of 12.9 grams of solid sulfur from 23.6 to 38.1 degrees Celsius. The specific heat of sulfur calculated from her data is J / g°C.
failedAnswered
Question 2 (1 point) In experiments, the fundamental attribution error has been demonstrated by people's tendency to underestimate the extent to which others' behavior is influenced by A) cognitive dissonance. B) assigned roles. C) attitudes. D) personality traits.
failedAnswered
[ Multiple Choice Question The glossopharyngeal nerve conveys information from the back of the tongue. O taste O tactile Need help? Review these concept resources. About the Concept your answer: High Medium Low © 2024 McGraw Hill. All Rights Reserved ]
failedAnswered
Which equation best matches the graph shown below?