Is It is not Monday and it is not Tuesday Equivalent to ~(P v Q)?

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SUMMARY

The discussion centers on the logical equivalence of the statement S: "It is not Monday and it is not Tuesday" to the expression ~(P v Q). The participant correctly identifies that ~(P v Q) is equivalent to (~P ∧ ~Q) and demonstrates this by constructing a truth table. The conclusion drawn is that since both expressions yield identical truth values, they are indeed tautologically equivalent.

PREREQUISITES
  • Understanding of logical operators: negation (~), disjunction (v), and conjunction (∧).
  • Familiarity with constructing truth tables for logical expressions.
  • Knowledge of tautologies in propositional logic.
  • Basic understanding of logical equivalence and its implications.
NEXT STEPS
  • Learn how to construct truth tables for complex logical expressions.
  • Study the principles of logical equivalence in propositional logic.
  • Explore tautologies and their significance in logical reasoning.
  • Investigate the use of logical operators in programming languages such as Python or Java.
USEFUL FOR

This discussion is beneficial for students of logic, mathematics, computer science, and anyone interested in understanding logical equivalences and truth tables.

joemama69
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Homework Statement


Find a statement for , S, equibalten to ~(P v Q) and show that it is logically equivalent by construction the truth table for "S if and only if ~(P v Q)" and showing that this statement form is a tautology.


Homework Equations





The Attempt at a Solution



My statement is

S: It is not Monday or it is not tuesday.

I'm not sure exactly how to set up the truth table. What would be my Column labels for S <-> ~(P v Q). Do in include the S or the <-> in the table.
 
Last edited:
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Note: ~(P v Q) is equivalent to (~P and ~Q). So your sample statement S does not work.
 
right right right

S:It is not monday and it is not munday ... ~(PvQ) <->(~P ^ ~Q) which are equil and because they are equal they will be a tautology.

is it correct to say they are a tautology becasue it will be all truths in the truth table which is because ~(PvQ) and (~P ^ ~Q) have equal truths (F,F,F,T) and then because they are the same (F,F,F,T) they are then all truths for ~(PvQ) <->(~P ^ ~Q) column
 

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