So it’s obviously correct to read P → Q as P only if Q. If, on the other hand, introduces a sufficient condition: P if Q means that the truth of Q is sufficient, or enough, for P to be true as well. That is, **P if Q rules out just one possibility: that Q is true and P is false**. But that is exactly what Q → P rules out.

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## What is the difference between if and only if and only if?

IF AND ONLY IF, is a biconditional statement, meaning that either both statements are true or both are false. So it is essentially and “IF” statement that works both ways. Note that **IF AND ONLY IF is different than simply ONLY IF**.

## Is P if and only if q the same as Q if and only if P?

It says that P and Q have the same truth values; when “P if and only if Q” is true, it is often said that **P and Q are logically equivalent**.

IF AND ONLY IF.

P | Q | P if and only if Q |
---|---|---|

T | T | T |

T | F | F |

F | T | F |

F | F | T |

## What do you call a statement P if and only if q?

In conditional statements, “If p then q” is denoted symbolically by “p q”; **p is called the hypothesis and q is called the conclusion**. For instance, consider the two following statements: If Sally passes the exam, then she will get the job. If 144 is divisible by 12, 144 is divisible by 3.

## What is if and only if statement?

In logic and related fields such as mathematics and philosophy, “if and only if” (shortened as “iff”) is **a biconditional logical connective between statements, where either both statements are true or both are false**.

## What is the negation of P if and only if q?

The negation of ‘p if and only if q’ is ‘**p and not-q**, or q and not-p,’ which, as it happens, is semantically equivalent to the exclusive disjunction, ‘p | q. ‘

## What does ↔ mean in math?

Symbol ↔ or ⟺ **denote usually the equivalence**, commonly known also as “NXOR”, “if and only if” or “iff” for short (see also its Wikipedia page). More precisely p↔q is equal to (p→q)∧(q→p)

## What is the difference between conditional and biconditional?

A conditional statement is of the form “if p, then q,” and this is written as p → q. A biconditional statement is of the form “p if and only if q,” and this is written as p ↔ q.

## What is inverse conditional statement?

The inverse of a conditional statement is **when both the hypothesis and conclusion are negated**; the “If” part or p is negated and the “then” part or q is negated. In Geometry the conditional statement is referred to as p → q. The Inverse is referred to as ~p → ~q where ~ stands for NOT or negating the statement.

## What’s a biconditional statement?

Description. A biconditional statement is **one of the form “if and only if”, sometimes written as “iff”**. The statement “p if and only if q” means “p implies q” AND “q implies p”. That is, it is a conjunction of two individual conditional statements.

## Is the converse of an if and only if statement true?

The sentence “If q, then p” is called its converse. The sentence “p if and only if q” means: If p then q and if q then p. In other words, it means that **a sentence and its converse are both true**.

## What is the truth value of the compound proposition P → Q ↔ P if P is false and Q is true?

Tautologies and Contradictions

Operation | Notation | Summary of truth values |
---|---|---|

Negation | ¬p | The opposite truth value of p |

Conjunction | p∧q | True only when both p and q are true |

Disjunction | p∨q | False only when both p and q are false |

Conditional | p→q | False only when p is true and q is false |

## What are the truth values for ~( p ∨ Q?

So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p.

Truth Tables.

p | q | p∨q |
---|---|---|

T | F | T |

F | T | T |

F | F | F |

## Is ~( p q the same as P Q?

~(P&Q) is **not the same as (~P&~Q)**. You can do this for any logic, and it saves a lot of time waiting for answers from StackExchange!

## What does P → Q mean?

The implication p → q (read: p implies q, or if p then q) is the state- ment which asserts that **if p is true, then q is also true**. We agree that p → q is true when p is false. The statement p is called the hypothesis of the implication, and the statement q is called the conclusion of the implication.

## Is ~( Pvq and PV Q the same?

Well, what does it mean to say not both? It means that either p is false or q is false or they are both false–anyway, p and q can’t both be true at the same time. So ~(p · q) º ~p v ~q. On the other hand, **~(p v q) means it’s not the case that either p or q**.

## Which is logically equivalent to P ↔ Q?

P → Q is logically equivalent to **¬ P ∨ Q** . Example: “If a number is a multiple of 4, then it is even” is equivalent to, “a number is not a multiple of 4 or (else) it is even.”

## Are the statements P ∧ Q ∨ R and P ∧ Q ∨ R logically equivalent?

Since columns corresponding to p∨(q∧r) and (p∨q)∧(p∨r) match, **the propositions are logically equivalent**. This particular equivalence is known as the Distributive Law.

## Does P follow from Pvq?

**p v q stands for p or q** That is: p v q iff at least one of p or q is true. Note that they may both be true. p ↔ q or p ≡ q stands for p iff q That is: p ↔ q iff either both p and q are true or both p and q are false, i.e. p has the same ‘truth value’ as q.

## Is p ∧ p ∨ q )) → QA tautology?

∵ **All true ∴ Tautology proved**.

## Is P → Q ∨ q → p a tautology?

(p → q) ∧ (q → p). (This is often written as p ↔ q). Definitions: **A compound proposition that is always True is called a tautology**.

## Which of the proposition is p ∧ P ∨ Q is?

The proposition p∧(∼p∨q) is: **a tautology**. **logically equivalent to p∧q**.

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tags | tag:apple |
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force match |
+apple |

views | views:100 |

score | score:10 |

answers | answers:2 |

## What is P and Q in logic?

**The proposition p is called hypothesis or antecedent, and the proposition q is the conclusion or consequent**.