# Is the set of all true contingent propositions equal to the set of all true propositions?

Contents

## What is a propositional truth?

Classical (or “bivalent”) truth-functional propositional logic is that branch of truth-functional propositional logic that assumes that there are are only two possible truth-values a statement (whether simple or complex) can have: (1) truth, and (2) falsity, and that every statement is either true or false but not both

## What are the properties of proposition?

Propositions represent (as do sentences, stories, perceptions, and so on), and they have truth-conditions. Properties don’t represent—they just have instantiation-conditions.

## 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.

## Do all true beliefs count as propositional knowledge?

A true belief may stem just from lucky guesswork; in that case it will not qualify as knowledge. Propositional knowledge requires that the satisfaction of its belief condition be suitably related to the satisfaction of its truth condition.

## 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”.

## Can a proposition be both true and 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.

## How do you determine if a proposition is true or false?

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.

## What is the difference between proposition and propositional logic?

A quantified predicate is a proposition , that is, when you assign values to a predicate with variables it can be made a proposition.
Difference between Propositional Logic and Predicate Logic.

Propositional Logic Predicate Logic
3 A proposition has a specific truth value, either true or false. A predicate’s truth value depends on the variables’ value.

## Is the same truth value under any assignment of truth values to their atomic parts?

Logical Equivalence.
That is, P and Q have the same truth value under any assignment of truth values to their atomic parts.

## What do you call two propositions with the same truth values?

Logically Equivalent: ≡ Two propositions that have the same truth table result. Tautology: A statement that is always true, and a truth table yields only true results.

## How do you determine the truth values of propositions?

Any proposition has two possible values True (T) or False (F). The negation of a proposition p is the proposition (denoted ~ p) that makes the opposite of p. A Truth Table is a table with a row for each possible set of truth values for the proposition being considered.

## How many of the propositions within a conditional proposition are conditional?

two propositions

A conditional assertion is not a standard kind of speech act (assertion) with a distinctive kind of content (a conditional proposition), but rather a distinctive kind of speech act that involves just the two propositions, the ones expressed by the antecedent and the consequent.

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

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

## How many different truth tables of the compound propositions are there that involve the propositions?

Since there are 4 rows and since each row has two possible truth values (true T or false F), there are 2 × 2 × 2 × 2 = 2 4 = 16 2\times 2\times 2\times 2=2^4=16 2×2×2×2=24=16 possible (different) truth tables.

## Which of the following compound propositions is logically equivalent?

The proposition ¬q → ¬p is called the Contrapositive of the proposition p → q. They are logically equivalent.

## How many different truth tables are possible for prepositions with 3 variables?

Constructing Truth Tables
If there are two variables (p, q), then you will need 22 or 4 rows. If there are three variables (p, q, and r), you will need 23 or 8 rows.

## What is the proposition PQ PQ a a tautology B a contradiction C a contingency D none of these?

The proposition p rarr ~(p^^q)” is “a tautology contradiction. neither tautology nor contradiction.

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

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. In other words, they ate both not true.

## Are the statements P → q ∨ R and P → q ∨ P → 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.