Examples of 'if and only if it' in a sentence
Meaning of "if and only if it"
if and only if - A phrase used in logic and mathematics to indicate that one statement is true only if another statement is true as well. It emphasizes the conditionality and exclusivity of the relationship between the two statements
How to use "if and only if it" in a sentence
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if and only if it
A matrix has a logarithm if and only if it is invertible.
If and only if it advances the plot . Notjust some arbitrary nudity.
A tuple is coprime if and only if it is coprime as a set.
An infinitely generated module is stably free if and only if it is free.
A belief is true if and only if it corresponds to a fact.
A function on a connected set is locally constant if and only if it is constant.
Domain if and only if it has no zero divisors.
An infinite word is recurrent if and only if it is a sesquipower.
If and only if it is at level formula 15 of the arithmetical hierarchy.
It is self contradictory if and only if it is logically false.
If and only if it has a constant solution λ > 0.
A proposition is true if and only if it corresponds to reality.
A topological space admits a separated uniform structure if and only if it is Tychonoff.
A ring is semisimple if and only if it is artinian and is semiprimitive.
In normed spaces a linear operator is continuous if and only if it is bounded.
See also
A monoid is free if and only if it is graded and equidivisible.
A linear operator on a metrizable vector space is bounded if and only if it is continuous.
It would true if and only if it is false.
For example, a principal bundle has a global section if and only if it is trivial.
A sentence is open if and only if it has free variables.
According to the Gromov-Ruh theorem, M is almost flat if and only if it is infranil.
A set is recursive if and only if it is at level of the arithmetical hierarchy.
A commutative ring is left primitive if and only if it is a field.
A graph is chordal if and only if it has a perfect elimination ordering.
A manifold admits a nowhere vanishing volume form if and only if it is orientable.
A kite is cyclic if and only if it has two right angles.
A topological space has a Hausdorff compactification if and only if it is Tychonoff.
A number is normal if and only if it is simply normal in every base.
An indifference graph has a Hamiltonian cycle if and only if it is biconnected.
A class is extensional if and only if it is characterized solely by its membership.
A matrix that has only real entries is Hermitian if and only if it is symmetric.
A function is harmonic if and only if it is both subharmonic and superharmonic.
Theorem A matrix is orthogonally diagonalizable if and only if it is symmetric.
A relation is asymmetric if and only if it is both antisymmetric and irreflexive.
Thus if n is odd, a cyclic polygon is equiangular if and only if it is regular.
A graph is a pseudoforest if and only if it does not contain a bicycle as a subgraph.
A k-regular sequence takes on finitely many values if and only if it is k-automatic.
Basis if and only if it is unitary.
A discrete space is compact if and only if it is finite.
Then is true if and only if it is false, which is a contradiction.
A transitive relation is asymmetric if and only if it is irreflexive.
If and only if it is non-empty.
A statement is analytic if and only if it is logically true.
If and only if it has property ∗.
And right simple if and only if it is a group.
A collection of subsets of X is a topology on X if and only if it generates itself.
A theory is true if and only if it corresponds with the facts.
In a complete logic, a formula is contradictory if and only if it is unsatisfiable.
It matches r if and only if it is followed by an s.
A right triangle is also a scalene triangle if and only if it is not isosceles.
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Examples of using Only
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Only yesterday he cussed me out something fierce
If she would only learn to behave herself
Only thing possessing him was a sixer of pabst
