## What does P → Q mean in math?

The proposition p is called **hypothesis or antecedent, and the proposition q is the conclusion or consequent**. Note that p → q is true always except when p is true and q is false.

## How do you read Pvq?

(p v q) is a proposition, call it r, so read **~(p v q)** as “it is not the case that the proposition r is true”. p and q are also propositions, so e.g. ~p is the proposition “it is not the case that p”. Read [(~p) v (~q)] as “it is the case that either (it is not the case that p) or (it is not the case that q).

## How do you negate an OR statement?

One thing to keep in mind is that if a statement is true, then its negation is false (and if a statement is false, then its negation is true).

Summary.

Statement | Negation |
---|---|

“A or B” | “not A and not B” |

“A and B” | “not A or not B” |

“if A, then B” | “A and not B” |

“For all x, A(x)” | “There exist x such that not A(x)” |

## What is the logical equivalent of P ↔ q?

⌝(P→Q) is logically equivalent to **⌝(⌝P∨Q)**. Hence, by one of De Morgan’s Laws (Theorem 2.5), ⌝(P→Q) is logically equivalent to ⌝(⌝P)∧⌝Q.

## What is 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.”

## Is P → Q ↔ P a tautology a contingency or a contradiction?

**Two compound propositions, P and Q, are said to be logically equivalent if and only if the proposition P ↔ Q is a tautology**. The assertion that P is logically equivalent to Q will be expressed symbolically as “P ≡ Q”. For example, (p → q) ≡ (¬p ∨ q), and p ⊕ q ≡ (p ∨ q) ∧ ¬(p ∧ q).

## Which of the following is a contradiction?

∴**(p∧q)∧∼(p∨q)** is a contradiction.

## Is PQ equivalent to (~ P → Q justify?

**Two propositions p and q are logically equivalent if their truth tables are the same**. Namely, p and q are logically equivalent if p ↔ q is a tautology.

## Are the statements P → Q ∨ R and P → Q ∨ P → are 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.

## Which of the following is logically equivalent to ∼ p → p ∨ ∼ q )]?

∴∼(∼p⇒q)≡**∼p∧∼q**.

## Which of the following propositions is tautology Pvq → Qpv Q → P PV P → Q Both B & C?

The correct answer is option (d.) **Both (b) & (c)**. Explanation: (p v q)→q and p v (p→q) propositions is tautology.

## Which of the proposition is p (~ Pvq is a Tautulogy a contradiction logically equivalent to p q All of above?

Which of the proposition is p^ (~ p v q) is

1) | A contradiction |
---|---|

2) | A tautulogy |

3) | All of above |

4) | Logically equivalent to p ^ q |

5) | NULL |

## Which of the following is not a contradiction Mcq?

4. If A is any statement, then which of the following is not a contradiction? Explanation: **A ∨ F** is not always false. Explanation: Definition of contingency.

## 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 can we directly say about proposition P1?

**What can we correctly say about proposition P1:P1 : (p v Ë¥q) ^ (q →r) v (r v p)**

- P1 is satisfiable.
- P1 is tautology.
- If p as true and q is true and r is false, then P1 is true.
- If p is true and q is false and r is false, the P1 is true.

## Which of the following pairs of propositions are not logically equivalent?

Hence the above statement is True, Logically not equivalent. ∴ Hence the correct answer is **((p ∧ q) → r ) and ((p → r) ∧ (q → r))**.

## How do you know if two propositions are logically equivalent?

The propositions are equal or logically equivalent **if they always have the same truth value**. That is, p and q are logically equivalent if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa. If p and q are logically equivalent, we write p = q.

## Which pair is logically equivalent?

Two logical statements are logically equivalent **if they always produce the same truth value**. Consequently, p≡q is same as saying p⇔q is a tautology. Beside distributive and De Morgan’s laws, remember these two equivalences as well; they are very helpful when dealing with implications. p⇒q≡¯q⇒¯pandp⇒q≡¯p∨q.

## What is not logically equivalent?

A conditional statement is not logically equivalent to **its inverse**. Only if : p only if q means “if not q then not p, ” or equivalently, “if p then q.” Biconditional (iff):

## How do you prove logical equivalence?

Two logical statements are logically equivalent **if they always produce the same truth value**. Consequently, p≡q is same as saying p⇔q is a tautology.

## What is the negation of P → Q?

The negation of “P and Q” is “**not-P or not-Q**”.

## Can two false sentences be logically equivalent?

**No two false sentences are logically equivalent**. circumstances. A pair of equivalent sentences must both be false at the same time if they are false at all.

## What is a logical contradiction?

A logical contradiction is **the conjunction of a statement S and its denial not-S**. In logic, it is a fundamental law- the law of non contradiction- that a statement and its denial cannot both be true at the same time. Here are some simple examples of contradictions. 1. I love you and I don’t love you.

## Are all logically indeterminate sentences logically equivalent?

**A sentence is logically indeterminate just if it is neither logically true nor logically false**. An argument is valid just if it is not possible for the premises to be true and the conclusion false. This may be the case when the conclusion is logically indeterminate.

## When two sentences are never both true at the same time those two sentences are said to be?

If two sentences cannot be both true at the same time (form **an inconsistent set**), they are said to be contrary.

## What is contradiction in truth table?

Contradiction A statement is called a contradiction **if the final column in its truth table contains only 0’s**. Contingency A statement is called a contingency or contingent if the final column in its truth table contains both 0’s and 1’s.

## Is contradiction always false?

**A contradiction is something that is always false**, regardless of it’s truth values.