 Welcome to our session. Let us discuss the following question. The question says for e j's and boolean algebra b, proof that x plus y equals to 1 and x dot y equals to 0 implies y is equal to x complement. Let us now begin with the solution. Now we will first consider x complement. X complement can be written as x complement plus 0 because 0 is identity for plus x and we are given that x dot y is equal to 0 complement plus complement.