If p and q are statements, the statement ‘p implies q’ or ‘if p then q’ is an implication and is denoted by p ⇒ q. It is reckoned to be false only in the case when p is true and q is false. So its truth table is as follows:
p is said to be sufficient for q and q to be necessary for p.
Informally, the implications of a proposition p (or set of propositions S) are those propositions which one would accept in the schema ‘if p then…’, (or, if each of S, then…). These will include things accepted only because of common sense, things which are common knowledge or presupposed in some context, or a sense of what regularly happens (‘if we go to London we will get caught in the crowds’). Logic tries to codify what is implied by sets of propositions in the more rigorous sense of what cannot possibly be false if they are each true. See also implicature.
- Lagoon Nebula
- lag operator
- lag phase
- Lagrange, Comte Joseph Louis
- Lagrange, Comte Joseph Louis (1736–1813)
- Lagrange fluid dynamics
- Lagrange interpolation
- Lagrange, Joseph-Louis (1736–1813)
- Lagrange, Joseph‐Louis (1736–1813)
- Lagrange multiplier
- Lagrange multiplier (LM) test
- Lagrange multipliers
- Lagrange point
- Lagrange(-Tournier), Joseph Louis de (1736–1813)
- Lagrange’s equation
- Lagrange’s equations
- Lagrange’s Theorem
- Lagrange’s Theorem(sum of four squares)
- Lagrangian
- Lagrangian coherent structure
- Lagrangian current measurement
- Lagrangian derivative
- Lagrangian fluid dynamics
- Lagrangian point
- Lagrangian points