Question 1190470: MAT 145: Topics In Contemporary Math
QUESTION 6
Create a truth table for the following.
left parenthesis p rightwards arrow q right parenthesis logical and left parenthesis r space logical or space tilde p right parenthesis
(p --> q) ∧ (r V ~ p)
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
T = true
F = false
Here are some facts to memorize- p v q is false when both p and q are false together; otherwise it's true
- p ^ q is true when both p and q are true together; otherwise, it's false
- p -> q is false when p is true and q is false; otherwise it's true
- ~p is the opposite of column p (i.e. flip everything in column p)
With all that in mind, we have this truth table
| p | q | r | ~p | p -> q | r v ~p | (p -> q) ^ (r v ~p) | | T | T | T | F | T | T | T | | T | T | F | F | T | F | F | | T | F | T | F | F | T | F | | T | F | F | F | F | F | F | | F | T | T | T | T | T | T | | F | T | F | T | T | T | T | | F | F | T | T | T | T | T | | F | F | F | T | T | T | T |
Notice we need 8 rows because of the 3 variables (p,q,r).
2^3 = 8
Column p has four T's in a row, followed by four F's in a row.
Column q has two copies of TTFF
Column r has four copies of TF
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