SOLUTION: Truth tables Use a truth table to show that: ~(𝑝 β†’ π‘ž) ≑ π‘βˆ§βˆΌπ‘ž

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Question 1170589: Truth tables
Use a truth table to show that:
~(𝑝 β†’ π‘ž) ≑ π‘βˆ§βˆΌπ‘ž
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

~(π‘β†’π‘ž) ≑ π‘βˆ§βˆΌπ‘ž

𝑝|π‘ž|π‘β†’π‘ž|~(π‘β†’π‘ž)|βˆΌπ‘ž|π‘βˆ§βˆΌπ‘ž|~(π‘β†’π‘ž)β‰‘π‘βˆ§βˆΌπ‘ž|
T|T| T |F     |F | F   |      T    |
T|F| F |T     |T | T   |      T    |   
F|T| T |F     |F | F   |      T    |
F|F| T |F     |T | F   |      T    |

This is true in all 4 cases, so it's called a tautology".

Rules  (You should learn them).
 
~  means to change what follows ~ to F if it's T, and to T if it's F.

β†’  means to put T in all cases except when there's a T on the left of β†’ and an F on the right of β†’.

≑  means to put a T if the same letter (T or F) is on both sides of ≑.

∧  means to put an F unless there are T's on both sides, then you put T.

v  means to put a T unless there are F's on both sides, then you put F (There were none of these v in this problem.)

Edwin