Help, find a statement using a truth table

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SUMMARY

The discussion centers on expressing a logical statement S in symbolic form based on a provided truth table. The truth table includes variables p, q, r, and S, with specific combinations of truth values leading to the output of S. The recommended approach is to construct a disjunctive normal form (DNF) expression for S by combining all instances where S is true, specifically using logical operators such as conjunction (AND) and disjunction (OR). Simplification of the resulting expression is also advised for clarity and efficiency.

PREREQUISITES
  • Understanding of truth tables and their structure
  • Familiarity with logical operators: AND, OR, NOT
  • Knowledge of disjunctive normal form (DNF) in propositional logic
  • Basic skills in symbolic logic notation
NEXT STEPS
  • Study the construction of disjunctive normal form (DNF) expressions
  • Learn about simplification techniques for logical expressions
  • Explore the application of truth tables in digital circuit design
  • Investigate the relationship between symbolic logic and Boolean algebra
USEFUL FOR

Students of mathematics and engineering, particularly those studying logic, propositional calculus, or digital circuit design, will benefit from this discussion.

jhlee127
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i don't understand how i can find a statement in given truth table.

p | q | r | S |
==========
T | T | T | F|
T |T | F | T |
T | F | T | T |
T | F | F | F |
F | T | T | T |
F | T | F | F |
F | F | T | T |
F | F | F | F |


please help me.
 
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jhlee127 said:
i don't understand how i can find a statement in given truth table.
I assume you mean "I don't understand how to express the statement S in symbolic form when given the following truth table."

If you can't make a clever guess for S, you could simply write it as a big "or" statement containing all the cases when it is true:

S \equiv (p \land q \land \lnot r) \lor (p \land \lnot q \land r) \lor ... etc.

then try to simplify the symbolic statement.

Are you studying logic in course on mathematics or are you studying logic in an engineering course in order to design logic circuits?
 

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