Propositional logic · Definition

Conjunction

logicpropositional

Before you start you need to know

Conjunction is one of the basic operations of mathematical logic. It combines two propositions into a single statement.

Definition

Given propositions \(P\) and \(Q\), their conjunction is the proposition \(P\land Q\).

\[P\land Q\]

Conjunction, also called "logical and", joins two propositions with the idea of "and". It is true only when both propositions it joins are true at the same time.

In an expression \(P\land Q\), each component keeps its own truth value and the conjunction computes a single result from both.

This operation formalizes statements that must hold simultaneously. If one of the two fails, the whole conjunction fails.

Think about it

What information is enough to make \(P\land Q\) true?

That \(P\) is true and \(Q\) is true under the same assignment.

Exercises 11

  1. \(P\land Q\) is true when...
  2. If \(P\) is true and \(Q\) is false, \(P\land Q\) is...
  3. Which symbol represents conjunction?
  4. The conjunction of \(P\) with itself is equivalent to...
  5. Which expression is a conjunction?
  6. What is the negation of «\(P\) and \(Q\)»?
  7. If \(P\) is false, \(P\land Q\) is...
  8. Conjunction resembles the operation...
  9. Which assignment makes \(P\land Q\) true?
  10. Which formula is equivalent to \(Q\land P\)?
  11. Is \(\lnot(P\land Q)\equiv\lnot P\land\lnot Q\) a logical equivalence?

What comes next

References

  • Frederic P. Schuller, Lectures on the Geometrical Anatomy of Theoretical Physics · Lecture 1, Introduction / Logic of Propositions and Predicates, YouTube, 2015.