Logic: Is P or Q Equal to P XOR Q?

[bomba923]

Given
$$P \to \neg \, Q$$

Is
$$P \vee Q \equiv P \oplus Q \text{ ?}$$

 

[0rthodontist]

The second symbol there is XOR?

P -> ~Q
~P v ~Q
P v Q
(~P v ~Q) n (P v Q)
P XOR Q

P -> ~Q
P XOR Q
(~P v ~Q) n (P v Q)
P v Q

Yes, they are equivalent.

 

[bomba923]

I see ; there's no difference between the two statements (given that condition)

The second symbol there is XOR?

Correct; what symbol do you use for XOR ?

 

[loseyourname]

The second symbol there is XOR?

P -> ~Q
~P v ~Q
P v Q
(~P v ~Q) n (P v Q)
~(P n Q) n (P v Q)
P XOR Q

For the sake of thoroughness, shouldn't you add the step above? It more straightforwardly describes the meaning of "XOR."