Diccrete Math problem: finding a proposition given a specific truth table

In summary, the task is to find a proposition using only p, q, ¬ and the connective ∧ that matches the given truth table. The solution is p ∧ (q ∧ ¬p), which is true when p is true and q is true.
  • #1
nicnicman
136
0

Homework Statement



Find a proposition using only p, q, ¬ and the connective ∧ with the given truth table.

p q ?
T T F
T F F
F T T
F F T

Homework Equations





The Attempt at a Solution



There is a systematic way of solving these but this system requires the use of an 'OR'. Is there a systematic way of solving this with only 'ANDs' or do you just keep guessing till you get it right. There must be an easier way!
 
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  • #2


After analyzing the given truth table, I have determined that the proposition can be represented as:

p ∧ (q ∧ ¬p)

This can be read as "p and (q and not p)". This proposition is true only when p is true and q is true, regardless of the value of p.
 

Related to Diccrete Math problem: finding a proposition given a specific truth table

1. How do I find a proposition given a specific truth table?

To find a proposition given a specific truth table, you need to first analyze the truth table to determine the logical operators being used and the corresponding truth values. Then, you can construct a logical expression using those operators and truth values that would give the same truth table when evaluated.

2. What is the importance of finding a proposition from a truth table?

Finding a proposition from a truth table allows us to express complex logical statements in a concise and systematic manner. It also helps in understanding the logical structure and relationships between different propositions.

3. Are there any specific steps or methods for finding a proposition from a truth table?

Yes, there are certain steps that can be followed to find a proposition from a truth table. These include identifying the logical operators, constructing a logical expression using those operators and truth values, and verifying the truth table of the resulting proposition.

4. Can a truth table have more than one proposition that satisfies it?

Yes, a truth table can have multiple propositions that satisfy it. This is because there can be different logical expressions that can lead to the same truth table when evaluated.

5. Is finding a proposition from a truth table limited to discrete math problems only?

No, finding a proposition from a truth table is not limited to discrete math problems. It is a fundamental concept in logic and can be applied in various fields such as computer science, philosophy, and mathematics.

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