Does a proposition have to have a true conclusion?

FALSE. A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

Does a proposition have to be true or false?

We define a proposition (sometimes called a statement, or an assertion) to be a sentence that is either true or false, but not both.

Can a proposition be a conclusion?

The conclusion of an argument is that statement or proposition for which the premises are intended to provide support. (In short, it is the point the argument is trying to make.)

What is considered a proposition?

A proposition is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0). Notation: Variables are used to represent propositions. The most common variables used are p, q, and r. Discussion. Logic has been studied since the classical Greek period ( 600-300BC).

Is a proposition a true statement?

A proposition is a sentence that makes a claim that is either true or false. A proposition need not be true. It need not be the case that we can easily tell whether or not it is true or false.

What is a proposition that is always false?

A compound proposition is called a contradiction if it is always false, no matter what the truth values of the propositions (e.g., p A ¬p =T no matter what is the value of p.

Which of the following is not a proposition?

Solution: (3) Mathematics is interesting



Mathematics is interesting is not a logical sentence. It may be interesting for some people but may not be interesting for others. Therefore this is not a proposition.

What is a proposition that is always true?

Definitions: A compound proposition that is always true for all possible truth values of the propositions is called a tautology. A compound proposition that is always false is called a contradiction. A proposition that is neither a tautology nor contradiction is called a contingency.

How do you determine the truth value of a proposition?

Calculating the Truth Value of a Compound Proposition

  1. For a conjunction to be true, both conjuncts must be true.
  2. For a disjunction to be true, at least one disjunct must be true.
  3. A conditional is true except when the antecedent is true and the consequent false.

Which sentence is not a proposition?

*There are examples of declarative sentences that are not propositions. For example, ‘This sentence is false‘ is not a proposition, since no truth value can be assigned. For instance, if we assign it the truth value True, then we are saying that ‘This sentence is false’ is a true fact, i.e. the sentence is false.

Is proposition A contradiction?

; 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). This can be generalized to a collection of propositions, which is then said to “contain” a contradiction.

What is a contradictory proposition?

Two propositions are contradictory iff they cannot both be true and they cannot both be false.

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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How do you know it’s not a proposition?

*There are examples of declarative sentences that are not propositions. For example, ‘This sentence is false’ is not a proposition, since no truth value can be assigned. For instance, if we assign it the truth value True, then we are saying that ‘This sentence is false’ is a true fact, i.e. the sentence is false.

Is a statement that is always true?

A statement which is always true is called a tautology. A statement which is always false is called a contradiction. For example, p ∧ (¬p) is a contradiction, while p ∨ (¬p) is a tautology.

Is the statement This statement is false a proposition?

“This statement is false” is not a proposition. S⟺¬S is a contradiction for any proposition S. @K. Hotz No it’s not, it’s a false proposition (a proposition that you can reduce to false).

What is the truth value of a true proposition?

If a proposition is true, then we say it has a truth value of “true”; if a proposition is false, its truth value is “false”. For example, “Grass is green”, and “2 + 5 = 5” are propositions. The first proposition has the truth value of “true” and the second “false”.

What is proposition logic?

The simplest, and most abstract logic we can study is called propositional logic. • Definition: A proposition is a statement that can be either true or false; it must be one or the other, and it cannot be both.

What are the simple proposition?

Simple propositions are declarative sentences which do not contain a connective. The restriction to declarative sentences is important. In propositional logic each proposition, simple or complex, must be capable of being either true or false. So we won’t count questions or commands, for example, as simple propositions.

How do you write a proposition?

How to Write a Value Proposition

  1. Identify your customer’s main problem.
  2. Identify all the benefits your product offers.
  3. Describe what makes these benefits valuable.
  4. Connect this value to your buyer’s problem.
  5. Differentiate yourself as the preferred provider of this value.


Is every sentence a proposition?

Not all sentences are propositions, propositions express sentence. Sentence is a proposition only in condition when it bears truth values i.e. true or false. We use English sentences governed by imprecise rule to state the precise rules of proposition.

How do you represent propositions?


And Q or y&z stand for the entire proposition. And not for the words within the proposition. Itself third and last we need to put proper punctuation. And negation if necessary.

How do you use proposition in a sentence?

Examples of proposition in a Sentence



Noun He made an attractive business proposition. The other company rejected their proposition. Her theory rejects the basic proposition that humans evolved from apes. If we accept proposition “A” as true, then we must accept proposition “B” as false.

What is proposition in elementary logic?

Proposition: a sentence that makes an assertion, a claim. Premise: a proposition that conditions a conclusion. Syllogism: an argument with two premises leading to a conclusion. Valid Argument: one in which the conclusion follows from the premises.

What is proposition in symbolic logic?

Symbolic logic is a shorthand way to change logical expressions into basic symbols and remove the ambiguity that comes with using a language. The smallest logical expression that cannot be broken down further without a loss of meaning is a proposition.

What is the difference between statement and proposition?

The difference is that statements merely express propositions. So a statement is “true” in virtue of the proposition it expresses being true. That is why only propositions are truth-bearers, while things like statements, thoughts, or ideas are not.

How do you know if a compound proposition is true?

A bi-conditional proposition is a compound proposition which consists of 2 propositions joined by the connective phrase “if and only if.” It is read as “p if → and only if q.” The word equivalence implies the truth value is true if the propositions have the same truth value.