Basic doubt on Modus Tollens Logical Implication

Question

P: Raju Attends Class
Q: Rani Attends Class

$P \rightarrow Q$  : If Raju Attends the Class, then Rani will attend class.

For Modus Tollens implication we will consider
($P \rightarrow Q$) $\Lambda$(~Q) $\Leftrightarrow$ ~P

But why can't we consider

($P \rightarrow Q$) $\Lambda$(~P) $\Leftrightarrow$ <what could be conclusion here>

Answer 1

P→Q  : If Raju Attends the Class, then Rani will attend class.

lets first explain this statement more

P	Q	P→Q
T	T	T
T	F	F
F	T/F	T

If Raju Attends the Class, then Rani will attend class means if Raju attends then Rani definitely attends but if Raju dosnt attend then Rani may or may not attend.

now explain given compound propositions

(P→Q) Λ(~Q) ⇔ ~P

"If Raju Attends the Class, then Rani will attend class" AND "Rani doesnt attend class"

if Rani doesnt attend then surely Raju doest becoz Rani attend only if Raju attend

as we know (P→Q) ⇔( ~Q→~P)            [contrapositive of (P→Q) ]

so above proposition ans is Raju doesnt attend (~Q)

 

(P→Q) Λ(~P) ⇔ <what could be conclusion here>

"If Raju Attends the Class, then Rani will attend class" AND "Raju doesnt attend class"

if Raju doesnt attend then Rani may or may attend (see from the table)

if Raju attend then Rani definitely attend

Comments

Still i am confused.

if raju attends then rani defenitly attends. but

if raju does not attends then rani may or may not attend.

so that means rani attends the class irrespective of raju attending the class or not. but if he attends she defenitely attend.

how can we conclude, if rani not there then raju not there in modus tollens