Finding a logical statement from a truth table

[jhlee127]

i don't understand how i can find a statement in given truth table.

p | q | r | S |
==========
T | T | T | F|
T |T | F | T |
T | F | T | T |
T | F | F | F |
F | T | T | T |
F | T | F | F |
F | F | T | T |
F | F | F | F |


please help me.

 

[Stephen Tashi]

i don't understand how i can find a statement in given truth table.

I assume you mean "I don't understand how to express the statement S in symbolic form when given the following truth table."

If you can't make a clever guess for S, you could simply write it as a big "or" statement containing all the cases when it is true:

$S \equiv (p \land q \land \lnot r) \lor (p \land \lnot q \land r) \lor ...$ etc.

then try to simplify the symbolic statement.

Are you studying logic in course on mathematics or are you studying logic in an engineering course in order to design logic circuits?