Conditions after Integration -- are they consistent?

Questions
,
1

Assuming[{p, m, [CapitalLambda], k} [Element] Reals, Integrate[k/(2 (k^2 + m^2) (-k + p)), {p, 0, [CapitalLambda]}]]

Mathematica’s answer is

ConditionalExpression[(k Log[1 - \[CapitalLambda]/k])/(2 (k^2 + m^2)), \[CapitalLambda] == 0 || (\[CapitalLambda] <= 0 && (k >= 0 || k <= \[CapitalLambda])) || (k >= \[CapitalLambda] && k > 0) || (\[CapitalLambda] >= 0 && k <= 0)]

Question:

Are the different conditions separately true i.e. should the answer be read in terms of “Either \[CapitalLambda] = 0” OR “[CapitalLambda] < 0 and also k >= 0 and k<=[CapitalLambda]”?

2

it is an OR. So it means any of these conditions must be true for the answer given to be valid.

A==0 || (A<=0 &&(k>=0 || k<=A)) mean A==0 on its own is sufficient condition, OR
A<=0 AND any one of k>=0 OR k<=A

So if A<=0 AND k>=0 then this is a condition. Also if A<=0 AND k<=A then this is another condition. But if A<=0 and neither of K>=0 and k<=A are true, then the condition will fail. So check on the next OR from other ones. If any condition on its own is true, then it is sufficient.