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

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

Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and the second statement can also be true in its own context, they just both have to have the same meaning.

## Do equivalent statements have the same truth value?

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 does two statement are logically equivalent mean?

Two statement forms are called logically equivalent if, and only if, they have identical truth values for each possible substitution for their. statement variables.

### What two logic statements have the same truth value?

This has some significance in logic because if two propositions have the same truth table they are in a logical sense equal to each other – and we say that they are logically equivalent. So: ¬p∨(p∧q)≡p→q, or “Not p or (p and q) is equivalent to if p then q.”…Logically Equivalent Statements.

p q p→q
F F T

### What makes a statement equivalent?

Determine equivalent and non-equivalent statements Equivalent Statements are statements that are written differently, but hold the same logical equivalence.

Can two false sentences be logically equivalent?

No two false sentences are logically equivalent. A pair of equivalent sentences must both be false at the same time if they are false at all. Page 43. Focus on exercise sets 1 and 5.

#### What is logically equivalent to an IF THEN statement?

The contrapositive of a conditional statement of the form “If p then q” is “If ~q then ~p”. Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.

#### What does logically equivalent mean in logic?

From Wikipedia, the free encyclopedia. In logic and mathematics, statements and are said to be logically equivalent if they are provable from each other under a set of axioms, or have the same truth value in every model.

What does it mean the statements are equivalent?

Equivalent Statements are statements that are written differently, but hold the same logical equivalence. Case 1: “ If p then q ” has three equivalent statements.

## Is logically equivalent to?

Two expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we write X≡Y and say that X and Y are logically equivalent.

## How do you write a logically equivalent statement?

Are all logically true sentences logically equivalent?

Definition: a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false. A pair of sentences may turn out true under exactly the same circumstances.