I was trying to refresh my memory of bayes rule.
As far as I understand,
P(test is true| X) = sensitivity.
P(test is false|X) = specificity.
(Let me know if the above understanding is wrong)
Then I was unable to see if the following relationship should hold:
specificity = 1 - sensitivity
If not then some examples of where they are correlated and where they are not will be appreciated.
Lastly, if they have some correlation: does P(X) play a role in their correlation.