Satisfiable is **an adjective**. The adjective is the word that accompanies the noun to determine or qualify it.

## What is satisfiable in discrete mathematics?

A compound proposition is satisfiable if **there is an assignment of**. **truth values to its variables that renders the proposition true**.

## How do you know if a proposition is satisfiable?

A compound proposition P is satisfiable if **there is a truth assignment that satisfies P**; that is, at least one entry of its truth table is true.

### When compound proposition is satisfiable?

A compound proposition is satisfiable **if there is an assignment of truth values to its variables that make it true**. When no such assignments exist, the compound proposition is unsatisfiable. A compound proposition is unsatisfiable if and only if its negation is a tautology.

### When a proposition is satisfiable and valid?

A formula is valid if it is true for all values of its terms. Satisfiability refers to the existence of a combination of values to make the expression true. So in short, a proposition is satisfiable if there is at least one true result in its truth table, **valid if all values it returns in the truth table are true**.

### What are tautologies and contradictions?

**A compound statement which is always true is called** a tautology , while a compound statement which is always false is called a contradiction .

### Is valid also satisfiable?

A formula **is valid if it is true for all values of its terms**. Satisfiability refers to the existence of a combination of values to make the expression true. So in short, a proposition is satisfiable if there is at least one true result in its truth table, valid if all values it returns in the truth table are true .

### Is a contradiction satisfiable?

All contradictions are **invalid** and falsifiable but not vice-versa. All contingencies are invalid and falsifiable but not vice-versa. … All contingencies are satisfiable but not vice-versa. All contradictions are unsatisfiable and vice-versa.

### Is a tautology satisfiable?

All tautologies are valid and unfalsifiable and vice-versa. All tautologies **are satisfiable but not vice-versa**.

### What does Extinguishable mean?

Definitions of extinguishable. adjective. **capable of being extinguished or killed**. “an extinguishable fire” “hope too is extinguishable”

### What is a better word than satisfactory?

**adequate**, decent, fair, good, gratifying, satisfying, solid, suitable, tolerable, valid, all right, ample, appeasing, assuaging, assuasive, average, cogent, comfortable, competent, cool.

### Is SAT Undecidable?

In fact, we have no known algorithm to solve (complete solution) the SAT problem in polynomial time, although it is remotely possible, but **highly unlikely**, that one may exist. Note that every NP problem is decidable.

### How do you test entailment?

We can check for logical entailment by **comparing tables of all possible interpretations**. In the first table, eliminate all rows that do not satisfy premises. In the second table, eliminate all rows that do not satisfy the conclusion.

### Why is satisfiability important?

In computer science, satisfiability (often abbreviated SAT) is **the problem of determining whether there exists an interpretation that satisfies the formula**. In other words, it establishes whether the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to true.

### What is a satisfiable sentence?

We say that a sentence is **satisfiable if and only if it is valid or contingent**. In other words the sentence is satisfied by at least one truth assignment. We say that a sentence is falsifiable if and only if it is unsatisfiable or contingent. In other words, the sentence is falsified by at least one truth assignment.

### How can I prove my CNF is satisfiable?

How can we prove that a CNF sentence is satisfiable? **By showing that there is a satisfying assignment**, that is, an assignment of truth values to variables that makes the sentence true.

### What is satisfiable in artificial intelligence?

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is **the problem of determining if there exists an interpretation that satisfies a given Boolean formula**. … In contrast, “a AND NOT a” is unsatisfiable.

### What is a contradiction example?

A contradiction is a situation or ideas in opposition to one another. … Examples of a contradiction in terms include, “**the gentle torturer**,” “the towering midget,” or “a snowy summer’s day.” A person can also express a contradiction, like the person who professes atheism, yet goes to church every Sunday.

### What causes contradiction?

In traditional logic, a contradiction occurs **when a proposition conflicts either with itself or established fact**. … ; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition).

### What is contradiction and contingency?

If the proposition is true in every row of the table, it’s a tautology. **If it is false in every row, it’s a contradiction**. And if the proposition is neither a tautology nor a contradiction—that is, if there is at least one row where it’s true and at least one row where it’s false—then the proposition is a contingency.

### What does ⊨ mean?

In logic, the symbol ⊨, ⊧ or is **called the double turnstile**. It is often read as “entails”, “models”, “is a semantic consequence of” or “is stronger than”. It is closely related to the turnstile symbol. , which has a single bar across the middle, and which denotes syntactic consequence (in contrast to semantic).

### What is propositional equivalence?

Formally, Two propositions and are said to be logically equivalent **if is a Tautology**. The notation is used to denote that and. are logically equivalent. One way of proving that two propositions are logically equivalent is to use a truth table.

### What is valid formula?

A valid formula, often also called a theorem, **corresponds to a correct logical argument, an argument that is true regardless of the values of its atoms**. For example p ⇒ p is valid. No matter what p is, p ⇒ p always holds.