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

P, Q, ~P, ~Q, P v Q, ~ (P v Q), ~P ^ ~Q, ~(P v Q) <-> (~P ^ ~Q)In summary, we need to find a statement that is logically equivalent to ~(P v Q) and demonstrate this by creating a truth table for "S if and only if ~(P v Q)" and showing that it is a tautology. The statement S: It is not Monday or it is not Tuesday is not suitable, so we can use the statement S: It is not Monday and it is not Tuesday, which is equivalent to ~(P v Q) <-> (~P ^ ~Q) and will result in all
  • #1
joemama69
399
0

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.
 
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  • #2
Note: ~(P v Q) is equivalent to (~P and ~Q). So your sample statement S does not work.
 
  • #3
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
 

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

1. What is abstract math?

Abstract math is a branch of mathematics that deals with abstract concepts and structures, rather than specific numbers or measurements. It focuses on the study of patterns, relationships, and structures in a more general and abstract way.

2. How is abstract math different from other branches of math?

Unlike other branches of math that deal with concrete and measurable quantities, abstract math focuses on concepts and structures that can be applied to a variety of situations and fields. It often uses symbols and notation to represent these abstract ideas.

3. What is a tautology in math?

A tautology in math is a statement or formula that is always true, regardless of the values of its variables. This is because the statement is logically true by definition or by the laws of logic, and therefore does not require any proof or justification.

4. Can you give an example of a tautology in math?

An example of a tautology in math is the statement "Either it is raining or it is not raining." This statement is always true, as it accounts for all possible scenarios and is logically true by definition.

5. How is tautology used in abstract math?

Tautologies are often used in abstract math as a way to prove or justify other statements or theorems. By using tautologies, mathematicians can build upon logically true statements to reach new conclusions and expand the understanding of abstract concepts and structures.

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