**How to check if two boolean expressions are equivalent**

- Parse the expresion storing it in some structure data.
- Reduce the expresion in OR groups.
- Check if the two expresions have the same groups.

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

Two statement forms are logically equivalent **if, and only if, their resulting truth tables are identical for each variation of statement variables**. p q and q p have the same truth values, so they are logically equivalent.

## What is the definition for two logical expressions being equivalent?

In logic, equivalency means that **two (or more expressions) are such that whenever one is true the other is and whenever one is false, the other is false**. In general, there are two ways to show that two things are equivalent. You could use logical reasoning, or a truth table.

## How do you find the equivalent statement?

Equivalent Statements are **statements that are written differently, but hold the same logical equivalence**. Case 1: “ If p then q ” has three equivalent statements. a) If it is blue, then it is the sky. It is not blue or it is the sky.

## Is logically inverse the same as conditional?

**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.”

## How do you prove tautology?

One way to determine if a statement is a tautology is to **make its truth table and see if it (the statement) is always true**. Similarly, you can determine if a statement is a contradiction by making its truth table and seeing if it is always false.

## Which statement 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.”

## Is tautology logically equivalent?

So, because tautologies always have the same truth value (namely, true), **they are always logically equivalent**.

## What is logically equivalent to the inverse?

Since an inverse is the contrapositive of the converse, **inverse and converse** are logically equivalent to each other.

## Which of the following is logically equivalent to an inverse statement?

**The converse** is logically equivalent to the inverse of the original conditional statement.

## What is the equivalent truth value of an inverse statement?

If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true. If two angles are congruent, then they have the same measure.

Converse, Inverse, Contrapositive.

Statement | If p , then q . |
---|---|

Inverse | If not p , then not q . |

Contrapositive | If not q , then not p . |

## Which statement has the same truth value as a conditional statement?

**The contrapositive** does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.

## 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.

## 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.

## When two statements are combined by logical connective if then then the compound statement is called?

So, the correct answer is that when two statement are connected connected by logical connective then the compound statement is called **conjunctive statement**.

## What is logic distinguish between sentence and proposition?

**Proposition is the unit of logic**. Proposition always comes in present tense. (sentences – all tenses) Proposition can explain quantity and quality. (sentences- cannot) Meaning of sentence is called proposition.