# Discrete math:propositional logic

1. Oct 10, 2009

### svishal03

1. The problem statement, all variables and given/known data
I want to construct a truth table for the following propositions

2. Relevant equations

(a) ¬p ∨ q
(b) p ∧ q ⇒ p
(c) ¬p ∨ q ⇔ p ⇒ q

3. The attempt at a solution

Approach:
1) Determine the order of precedence:

2) Fill in the values for the operator with the higher precedence:

3) Next fill in the values for the lower precedence

I guess, answer for a , b and c is:

(a) ¬p ∨ q
p q ¬p ∨q
t t f t
t f f f
f t t t
f f t t

(b) p ∧ q ⇒ p
p q p ∧ q ⇒ p
t t t t
t f f t
f t f t
f f f t

(c) ¬p ∨ q ⇔ p ⇒ q
p q ¬p ∨q ⇔ p ⇒ q
t t f t t t
t f f f t f
f t t t t t
f f t t t t

Is this right?

Further, can anyone explain intuitive statements to explain any of the above--say (a) and (b)---i.e reasoning out (a) and (b) truth table through example statements
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 10, 2009

### Elucidus

Your tables are not clear enough for me to make out exactly what you are doing. I'm also not convinved there is a precedence rule between $\Rightarrow$ and $\Leftrightarrow$. Part (c) may end up being ambiguous.

--Elucidus

3. Oct 11, 2009

### svishal03

Can you comment upon part (a) and (b) only at least?
(a) ¬p ^ q
p q ¬p ^q
t t f t
t f f f
f t t t
f f t t

(b) p ¬ q => p
p q p ¬ q => p
t t t t
t f f t
f t f t
f f f t

Can you give statements t prove the logic?Or making it independent of precedence, srating from a scratch, how would you go about?