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## How do you translate sentences into predicate logic?

*So something like jeffrey is happy again we could establish our keys. And we could say okay lowercase j is jeffrey.*

## How do you know if a predicate logic is valid?

An argument expressed with sentences in predicate logic is valid **if and only if the conclusion is true in every interpretation in which all the premises are true**.

## How do you translate sentences in logic?

*So i'm going to call this w for went even though the store was closed. So our second simple sentence here is the store was closed. So i'm going to call this c for closed.*

## What is an interpretation in predicate logic?

1 Interpretations

A sentence of a formal language (e.g., the propositional calculus, or the predicate calculus) is neither true nor false. By definition, an interpretation of a sentence of a formal language is **a specification of enough information to determine whether that sentence is true or false**.

## How can you change a predicate to proposition?

**Existential quantification** is yet another way of converting a predicate into a proposition. Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “P(x) is true for some x in the universe of discourse.” We write ∃ x P(x), and say “there exists x, P(x)”.

## What is predicate logic in discrete mathematics?

Predicate Logic – Definition

**A predicate is an expression of one or more variables defined on some specific domain**. A predicate with variables can be made a proposition by either assigning a value to the variable or by quantifying the variable. The following are some examples of predicates − Let E(x, y) denote “x = y”

## What are the limitations of predicate logic?

One key limitation is that **it applies only to atomic propositions**. There is no way to talk about properties that apply to categories of objects, or about relationships between those properties. That’s what predicate logic is for.

## Why do we use predicate logic?

Predicate logic **allows us to talk about variables (pronouns)**. The value for the pronoun is some individual in the domain of universe that is contextually determined.

## How do you negate predicate logic?

To negate a sequence of nested quantifiers, you **flip each quantifier in the sequence and then negate the predicate**. So the negation of ∀x ∃y : P(x, y) is ∃x ∀y : P(x, y) and So the negation of ∃x ∀y : P(x, y) and ∀x ∃y : P(x, y).

## How do you negate universal and existential quantification?

**The negation of a universal statement (“all are”) is logically equivalent to an existential statement (“Some are not”)**. Similarly, an existential statement is false only if all elements within its domain are false. The negation of “Some birds are bigger than elephants” is “No birds are bigger than elephants.”

## How do you negate implications?

Negation of an Implication.

The negation of an implication is a conjunction: **¬(P→Q) is logically equivalent to P∧¬Q**. ¬ ( P → Q ) is logically equivalent to P ∧ ¬ Q .