Select the correct alternative from the given choices. For non empty sets A and B, which of the

Select the correct alternative from the given choices. For...

Key Concepts

Set Complement

The set complement of an element is the collection of all elements not in the specified set relative to a universal set. This concept helps in understanding how sets interact with the rest of the elements in the universal context.

Set Difference

Set difference, denoted as A – B, identifies the elements that are in set A but not in set B. This operation is fundamental when determining unique elements that belong exclusively to one set.

Intersection

The intersection of two sets, represented as A ? B, consists of all elements that are common to both sets. It is a vital concept for identifying shared elements between groups.

Union

The union of sets, denoted as A ? B, is the aggregation of all elements that appear in either set A or set B, including those common to both. This operation is essential for combining sets into a complete collection.

Empty Set

The empty set is a set with no elements, often denoted by ?. Recognizing when set operations yield an empty set is important for understanding the outcomes of various set operations.

Transcript

00:01 Hello students our question is for non -empty set a and b which are the following is non -empty so we have given four options let's write the option let's write the option we have to prove that in option a that a difference a complement in option b a difference b intersection a intersection a intersection a difference b intersection a difference b intersection a difference b intersection a intersection b in option c we have meme that is universal set minus a union a complement and in option b we have a intersection a complement so we have to tell that which of these are non -amptice so let's draw the diagram we have the diagram here this is our set a this is our set b is our set a and this is our set b this will be our set a difference b let's do a difference b this is our set a difference b and now this will be this will be the universal set that is new this will be equal to this will be equal to a complement this is a complement so here we have the horizontal lines are a difference b a difference b and the vertical lines are the vertical lines are showing a complement and the plain area shows a intersection b now let's discuss one by one number one a a difference a complement so a difference a complement so a comprises of the elements which are present which are not present in here so if we take difference of those elements which are not present in a with the set a then this will be equal to set a here if we look at the diagram the difference of set a and a complement that is the vertical line is equal to set a so here set a will be of a difference b this will be equal to a difference b intersection a intersection so this will be a difference b this area and the area of a intersection b so not intersection union union a union union that is a difference b union a intersection b will be equal to set now this is not an empty set let's discuss the other set our b a difference b intersection a intersection so if we see the diagram a difference b will be the vertical horizontal lines and the a intersection b will be the area unshated area so there is no common area between a difference b and a intersection b so this is equal to or c mule that is universal set minus a union a complement a is the horizontal lines sorry a will be the area which comprises of the horizontal lines in the unshedit area and a difference will be the vertical lines so if we take difference of universal set with this area that is the horizontal line and the unschedied area in the vertical line so so we have null set here.

04:56 That is the universal set.

04:58 This is also equal to the universal set.

05:00 That is a union, a complement will be equal to universal set.

05:08 Then universal set minus universal set will be equal to null set.

05:12 So let's see the third option that is fourth option that is the a intersection, a complement will be equal to.

05:21 A intersection a complement...

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