Hello Friends,

I have a question concerning sentential logic:
It's said that a sentence is denoted by '(P-Q)' just in the case that there is a pair of sentences P and Q such that the sentence is true if either P is false or both P and Q are true and the sentence is false if P is true and Q is false.

For example if P = The price rice will rise and Q = the demand of rice will fall then if The price rice will rise then the demand of rice will fall can be denoted as P-Q.

I can not understand why the sentence remains true even if P is false? Can you please explain ?

Best Regards,
Sabya

Question

Hello Friends,

I have a question concerning sentential logic:
It's said that a sentence is denoted by '(P->Q)' just in the case that there is a pair of sentences P and Q such that the sentence is true if either P is false or both P and Q are true and the sentence is false if P is true and Q is false.

For example if P = The price rice will rise and Q = the demand of rice will fall then if The price rice will rise then the demand of rice will fall can be denoted as P->Q.

I can not understand why the sentence remains true even if P is false? Can you please explain ?

Best Regards,
Sabya

amistre64 · Answer

there is no condition placed upon P when it is false; the statement only provides conditions for if P is true

anonymous · Answer

Also, in math it is possible to start out with a "false" statement and end up with a "true" statement.
For example:

$$3\geq 5 \Rightarrow 3*0\geq 5*0 \Rightarrow 0\geq 0$$

anonymous · Answer

Not that it proves anything, its possible though.

amistre64 · Answer

its the difference between a conditional and a biconditional statement right?

amistre64 · Answer

"->" is conditional ; q depends on p

"<->" is bi conditional ; the if and only if stuff

amistre64 · Answer

p= it is raining
q = it is wet outside

if it is raining, then it is wet outside
            T                          T            =      T

if it is raining, then it is not wet outside
            T                           F             =     F

if it is not raining, then it is wet outside
             F                           T             =    T

if it is not raining, then it is not wet outside
             F                           F              =   T

if i see it correctly

akshay_budhkar · Answer

^ is and and V is or in logic if i am not wrong

amistre64 · Answer

^, n , U upside down; think of them as spelling out "A"nd

amistre64 · Answer

of course U or V is similar to spelling out "U"nion which is the or

akshay_budhkar · Answer

ya so the same is used in logic no?

amistre64 · Answer

this question tho has nothing to do with p.n.q or p.u.q

amistre64 · Answer

yep

amistre64 · Answer

.n. and .u. are connectors, operators, times and plus

-> and <-> are something else

akshay_budhkar · Answer

no i mean maybe yes
but in our course that we had we had ^ and v same as -> and <->
they were called and or if if else(iif)

anonymous · Answer

What amistre64 says makes sense here. P is te sufficient condition for Q and Q is the necessary condition for P.  But it's still not clear to me why if P is false or for that matter P and Q are bothr false - the sentence remains true.

amistre64 · Answer

i agree with you that it can be confusing, and so we simply restort to the definitional aspect of it.  :)