What does it mean for two sentences to be equivalent?
Saying that two statements are logically equivalent means that they invariably have the same truth value as each other. For example, if you are talking about propositional calculus such a statement could be p∧¬p.
How do you know if two statements are 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.
What are equivalent statements?
Equivalent Statements are statements that are written differently, but hold the same logical equivalence. Case 1: “ If p then q ” has three equivalent statements.
What statements are logically equivalent to each other?
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.
What is equivalent and example?
The definition of equivalent is something that is essentially the same or equal to something else. An example of equivalent is (2+2) and the number 4. Since 2+2= 4, these two things are equivalent. adjective.
How do you find the equivalent statement?
Take for example the statement “If is even, then is an integer.” An equivalent statement is “If is not an integer, then is not even.” The original statement had the form “If A, then B” and the second one had the form “If not B, then not A.” (Here A is the statement ” is even”, so “not A” is the statement ” is not even” …
What is the equivalent of a conditional statement?
A conditional statement is logically equivalent to its contrapositive. Converse: Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p.
What is equivalent to if/then statement?
A conditional statement is logically equivalent to its contrapositive. Suppose a conditional statement of the form “If p then q” is given. The converse is “If q then p.” Symbolically, the converse of p q is q p.
Which statement is equivalent with the 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….Converse, Inverse, Contrapositive.
| Statement | If p , then q . |
|---|---|
| Converse | If q , then p . |
| Inverse | If not p , then not q . |
| Contrapositive | If not q , then not p . |