In selection LR if the statement says "A is selected if and only if B is selected". Here according to me, there are 3 cases either both are selected, none of them is selected, or B is selected alone. But in the solution, it says that there are only two possibilities either A and B both are selected or neither is selected. Can anyone help me understand how only B cannot be selected?

it may seem to you that there will be 3 cases , "if and only if" means that one thing will be included only if the second thing is also included. example --"B is selected if and only if A is selected " in this case make a block of A and B.. either both of them will be included or neither will be included . You will have to make three cases if the statement says something like "if A is selected then B is also selected " .here there will be 3 cases

hi can u tell which lrdi set this is from? I agree with your statement that 3 cases are possible.

Consider this example,

CAT only if IIM

if CAT then IIM may or may not be possible
if no CAT then IIM definitely not possible
if IIM then CAT definitely
if no IIM then CAT may or may not be possible

Understood