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in this presentation we will continue our discussion on set identities and in this particular presentation we will start our discussion with d morgans laws so lets get started under this category we have two laws a union b complement equal to a complement intersection b complement a intersection b complement equal to a complement union b complement we have to prove these laws one by one they are very important for us to understand okay first we will prove a unit b complement is equal to a complement intersection b complement from the definition of complement we know that a union b complement is equal to set of all xs that x does not belong to a union b this is from the definition of complement right this is a union b complement this set is nothing but a set of all x such that x does not belong to a union b right we can easily replace this statement by this statement this is x does not belong to a union b we can write this as not of x belongs to a union b okay also you can see that