## What is tautology and contradiction in math?

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

## What is WFF math?

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language.

**What is tautology and satisfiable?**

A compound proposition P is a tautology if every truth assignment satisfies P, i.e. all entries of its truth table are true. 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.

**What is satisfiability in discrete mathematics?**

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 is WFF give example?

A Statement variable standing alone is a Well-Formed Formula(WFF). For example– Statements like P, ∼P, Q, ∼Q are themselves Well Formed Formulas. If ‘P’ is a WFF then ∼P is a formula as well. If P & Q are WFFs, then (P∨Q), (P∧Q), (P⇒Q), (P⇔Q), etc.

### How do you identify a WFF?

It has only three rules:

- Any capital letter by itself is a WFF.
- Any WFF can be prefixed with “~”. (The result will be a WFF too.)
- Any two WFFs can be put together with “•”, “∨”, “⊃”, or “≡” between them, enclosing the result in parentheses. (This will be a WFF too.)

**What is the satisfiability problem?**

Boolean Satisfiability Problem Boolean Satisfiability or simply SAT is the problem of determining if a Boolean formula is satisfiable or unsatisfiable. Satisfiable : If the Boolean variables can be assigned values such that the formula turns out to be TRUE, then we say that the formula is satisfiable.

**How do you write a wff?**

## How do you prove wff?

Well-formed formulas will be called “wffs”. Rule (1) A variable standing alone is a wff. Rule (2) If p is a wff, so is ~p. Rule (3) If p and q are wffs, (p∧q), (p∨q), (pÉq), and (p⇔q) are wffs….Valid wffs.

Law | wff |
---|---|

(p∨q) ⇔ ~(~p.~q) | |

Commutative Laws | (p∨q) ⇔ (q∨p) |

(p.q) ⇔ (q.p) | |

Associative Laws | [(p∨q)∨r] ⇔ [p∨(q∨r)] |

## What is wff give example?

**Is P & Q a wff?**

This is a wff: p∧(q∨r). So there are an infinite number of formulas that are not wffs, just as there are an infinite number that are wffs….Valid wffs.

Law | wff |
---|---|

De Morgan Laws | (p.q) ⇔ ~(~p ∨ ~q) |

(p∨q) ⇔ ~(~p.~q) | |

Commutative Laws | (p∨q) ⇔ (q∨p) |

(p.q) ⇔ (q.p) |

**What is tautology and example?**

Tautology is the use of different words to say the same thing twice in the same statement. ‘The money should be adequate enough’ is an example of tautology. Synonyms: repetition, redundancy, verbiage, iteration More Synonyms of tautology. COBUILD Advanced English Dictionary.

### Which formula is a tautology?

In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is “x=y or x≠y”. Similarly, “either the ball is green, or the ball is not green” is always true, regardless of the colour of the ball.

### Is Pvq → q tautology?

Look at the following two compound propositions: p → q and q ∨ ¬p. (p → q) and (q ∨ ¬p) are logically equivalent. So (p → q) ↔ (q ∨ ¬p) is a tautology.

**What are the rules of wff?**

It has only three rules:

- Any capital letter by itself is a WFF.
- Any WFF can be prefixed with “~”. (The result will be a WFF too.)
- Any two WFFs can be put together with “•”, “∨”, “⊃”, or “≡” between them, enclosing the result in parentheses. (This will be a WFF too.)

**What is the difference between tautology and satisfiable?**

Satisfiable can be a tautology or even if there is one True value in the truth table. Eg. p or (not p) is tautology and not (p implies q) has one True.

## What is a tautology in math?

Tautologies are typically found in the branch of mathematics called logic. They use their own special symbols: p p, ~p ~ p and q q all signify the statements, with p p generally reserved for the first one and either ~p ~ p or q q for the second statement. You can “translate” tautologies from ordinary language into mathematical expressions.

## Is a tautology always true?

No matter what the individual parts are, the result is a true statement; a tautology is always true. The opposite of a tautology is a contradiction or a fallacy, which is “always false”.

**What is the difference between satisfiable and unsatisfiable truth tables?**

Unsatisfiable means the truth table is a contradiction. ie. A wff which is not valid is unsatisfiable. Eg. p and (not p) Satisfiable can be a tautology or even if there is one True value in the truth table. Eg. p or (not p) is tautology and not (p implies q) has one True. So, they are satisfiable.