[LEARN] LOGICAL CONNECTIVES

[Peanutswar]

This topic is much related to the previous one I created which is the [LEARN] LOGIC GATES and chance to earn merit. if you understand the logic gates its easier for you to understand the concept of the truth table with logical connectives.

IMPLICATION(→) - the value will only become false, if X is true and Y is false.

P | Q | P → Q T | T | T F | T | T T | F | F

BI-CONDITIONAL(⇔) - The value will only become true if they are both true or both false.

P | Q | P ⇔ Q T | T | T F | T | F T | F | F F | F | T

NOT/NEGATION(¬)
Where you reverse the value of the given statement.

P | ¬P T | F F | T T | F

OR(V) either if there's a value of true the answer becomes true.

P | Q | P V Q T | T | T T | F | T F | T | T

AND(∧) either if there's a value of false the answer becomes false. The only possible becomes true if X and Y are true.

P | Q | P ∧ Q T | T | T F | T | F T | F | F

PROBLEM SOLVING

Let's try to solve this with the combination of both logical connectives.

(P → ¬Q) ∧ (P V Q)

P | Q | ¬Q | P → ¬Q | P V Q | (P → ¬Q) ∧ (P V Q) T | T | F | F | T | F T | F | T | T | T | T F | T | F | T | T | T F | T | F | T | T | T F | T | F | T | T | T

Here we go again for another challenge hoping that other members would really like to solve this kind of problem. Of course there's also a merited reward but only one per member who got the correct answer to become not abuse only 5 sMerit will be distributed.

(¬P ∧ ¬Q) → (P V Q)

P | Q | ¬P | ¬Q | ¬P ∧ ¬Q | P V Q | (¬P ∧ ¬Q) → (P V Q) T | F | T | T | T | T | F | F | F | T |

Other sources can help

Code:

https://www.tutorialspoint.com/mathematical-logical-connectives
https://courses.lumenlearning.com/math4libarts/chapter/truth-tables-and-analyzing-arguments-examples/
https://sites.millersville.edu/bikenaga/math-proof/truth-tables/truth-tables.html

[jackg]

Is there a reason why some are missed? Can you make it explicit.

Edit [removed just in case clue given]

[Peanutswar]

Is there a reason why some are missed? Can you make it explicit.

Edit [removed just in case clue given]

Are referring about logical operators like the ||, ! and &&. Or those like boolean algebra like this?

I made this image

[jackg]

Is there a reason why some are missed? Can you make it explicit.

Edit [removed just in case clue given]

Are referring about logical operators like the ||, ! and &&. Or those like boolean algebra like this?

I made this image

No. The truth table for implication, or and and are missing a set of inputs (false and false).