THE CONTRPOSITVE/NEGATION OF "AND"

[opubot]

Hello:
What is the contrpositive/negation of "and."
Thanks!

[tommywallach]

Hey Opubot,

Traditionally, "and" statements become "or" in the contrapositive. For example:

1. If X and Y, then Z.

Becomes-->

If not Z, not X or Y.
(Of course, remember that LSAT "or" also includes BOTH).

2. If X, then Y and Z.

Becomes-->

If not Y or Z, not X.

3. If not X and Y, then Z.

Becomes-->

If no Z, then X or Y.


Hope that helps!

-t

[waseemjutt647]

What is the contrpositive/negation of "and."

[tommywallach]

"And" can't have a contrapositive, because it isn't a statement. My examples show you how to contrapositive "and" in an actual statement.

-t

[luisjake47]

In logic, contraposition is a law that says that a conditional statement is logically equivalent to its contrapositive. Pass4sure 642-035 Exam The contrapositive of the statement has its antecedent and consequent inverted and flipped: the contrapositive of P \rightarrow Q is thus \neg Q \rightarrow \neg P . For instance, the proposition "All bats are mammals" can be restated as the conditional "If something is a bat, then it is a mammal". Now, the law says that statement is identical to the contrapositive "If something is not a mammal, then it is not a bat." Pass4sure 640-916

[z4zack120]

If you give this some thought, you can see it isn’t necessarily true. Just because monkeys always eat bananas doesn’t prevent other animals from eating bananas too. If we’re told that George eats bananas, George might be a monkey, or he might be any other banana-loving creature. This is a bad inference. Pass4sure 210-451 Exam Question
Technically, this is a logical fallacy called “affirming the consequent,” because it tries to offer the consequent as proof of something. But a consequent doesn’t do anything for you. Many things can lead to a consequent. Consider the statement, “if I have no gasoline, my car won’t start.” The consequent is that my car won’t start. But there could be many reasons why my car won’t start — no gas, no engine, it’s too cold. Pass4sure 220-901 Study Guide