Solving Formula for Truth Table: P & Q

In summary, the formula for this truth table with variables P and Q is P\vee(\negP\wedgeQ). This formula represents the exclusive or operation and is made up of minterms, which are expressions using conjunction and negation that are true for each line of the truth table with a true output. The disjunction of all minterms is the final formula.
  • #1
autre
117
0
I need to find the formula involving [itex]\neg[/itex], [itex]\wedge[/itex] or [itex]\vee[/itex] for the following truth table with the variables P and Q:

P Q formula
F F F
F T T
T F T
T T F

The closest I've gotten is something like P[itex]\vee(\neg[/itex]P[itex]\wedge[/itex]Q) which clearly doesn't work for the last row. Any ideas?
 
Physics news on Phys.org
  • #2
That's the truth table for "exclusive or".

¬P∧Q is only true with P = F and Q = T. (line 2)

P∧¬Q is only true with P = T and Q = F. (line 3)

These are what are known as minterms. Minterms are expressions using only conjunction and negation (∧ and ¬), which are true for the inputs from one line of the truth table with a true output. Each input should be represented in the minterm.

The disjunction (∨) of all minterms will be an expression that corresponds to the truth table.
 
Last edited:

1. What is the purpose of solving a formula for a truth table?

Solving a formula for a truth table helps to identify the logical relationships between different variables in a given statement. It allows for a clear understanding of the truth values of the statement based on different combinations of the variables.

2. How do you create a truth table for a given formula?

To create a truth table for a given formula, first identify all the variables present in the formula. Then, create a table with columns for each variable and a row for each combination of truth values for the variables. Finally, use the logical operators (such as AND, OR, NOT) to determine the truth value of the statement for each row.

3. What is the process for solving a formula for a truth table?

The process for solving a formula for a truth table involves breaking down the formula into smaller components, identifying the truth values for each component, and then combining them to determine the overall truth value of the statement. This is often done using a step-by-step approach, starting with the simplest components and working towards the more complex ones.

4. What is the significance of a truth table in logic and mathematics?

A truth table is a fundamental tool in logic and mathematics as it helps to determine the truth values of complex statements and equations. It also allows for the identification of logical relationships between different variables and can be used to prove or disprove arguments and theories.

5. Are there any limitations to using a truth table to solve formulas?

While truth tables are a useful tool, they can become very complex and time-consuming when dealing with multiple variables and operators. They also do not take into account the real-world context or assumptions that may affect the truth values of a statement. In these cases, other methods such as logical proofs or computer programs may be more effective for solving formulas.

Similar threads

MHB Calculating Truth Tables for Propositions
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
937
MHB Solving Q.7 with Truth Tables: What Is the Right Conclusion?
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
MHB Truth Table for P(x) & R(x), ~Q(x) & P(x) in U
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Understanding the truth table of → (implies)
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
I Proving the Implication of p and (p -> q) to q without Truth Tables
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
MHB Proof & Structure: Solve (¬ p V q) ↔ ( p Λ ¬ q) - John
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
961
B P → q with NOR operator and Constant F (false)
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
MHB Create a Truth Table: (p ^ q) ->(p ▼ ~q)
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
Truth table, implication and equivalence
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
3K
Logic Truth Table: Answers Checked
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
6K

Hot Threads

Recent Insights

Back
Top