 Welcome to our session. Let us discuss the following question. The question says if B is a Boolean algebra, xy belongs to B, then show the following. x plus y plus x complement dot y complement is equal to 1. Let's now begin with the solution. Now we will first consider the left-hand side. The left-hand side is equal to x plus y plus x complement dot y complement. Now this is equal to y plus x complement dot y complement by commutative law of plus. y complement by associative law of plus. y complement by distributive law of plus over dot plus y complement. Because for each x belonging to B, x complement is equal to 1. And this is equal to y plus x plus y complement dot 1 by commutative law of dot. y complement x belonging to B, x dot 1 is equal to x. equal to y plus x plus y complement by associative law of plus. y complement plus y plus x by commutative law of plus to y complement plus y plus x by associative law of plus. to 1 plus x because for x belonging to B, equal to 1. So similarly for each y belonging to B, y complement plus y is equal to 1. And this is equal to 1. Because for each x belonging to B, x is equal to 1. And this is equal to right-hand side. So we have proved that left-hand side is equal to right-hand side. So this completes the session. Bye and take care.