Solving Formula for Truth Table: P & Q

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SUMMARY

The discussion focuses on deriving a logical formula for the truth table of the exclusive OR (XOR) operation using the variables P and Q. The truth table indicates that the formula must yield true for the combinations (F, T) and (T, F) while being false for (F, F) and (T, T). The correct approach involves identifying minterms, which are expressions using conjunction (∧) and negation (¬) that correspond to true outputs in the truth table. The final expression is the disjunction (∨) of all relevant minterms.

PREREQUISITES
  • Understanding of logical operators: conjunction (∧), disjunction (∨), and negation (¬).
  • Familiarity with truth tables and their construction.
  • Knowledge of minterms and their role in logical expressions.
  • Basic principles of Boolean algebra.
NEXT STEPS
  • Research the construction of truth tables for various logical operations.
  • Learn about Boolean algebra simplification techniques.
  • Explore the concept of minterms and maxterms in detail.
  • Study the application of Karnaugh maps for simplifying logical expressions.
USEFUL FOR

This discussion is beneficial for students of logic, computer science professionals, and anyone interested in understanding Boolean functions and their representations in digital circuits.

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I need to find the formula involving \neg, \wedge or \vee 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\vee(\negP\wedgeQ) which clearly doesn't work for the last row. Any ideas?
 
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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.
 
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