 Hi and welcome to the session. Let us discuss the question which is given to us. It says show that a Intersection b is equal to a intersection c need not imply set b is equal to set c Now this question will be more clearer to us if we understand it with the help of a weighing diagram Let this be The universal set this be set a Set b and this be set c right now Just be very careful when I'm marking the Figure that I need to show it says a Intersection b now which is the area that represents a intersection b that is this area right is Equal to a Intersection c now, which is the area that is representing a intersection C that is overlapping of the figure that I have drawn plus This area also and it says that it need not imply that set b is Equal to set c that means all the elements of set b are there in set c That is very obvious with the given figure that I have drawn here So understanding the question with the help of this weighing diagram is the key idea that we're going to use in order to proceed on with our solution, right? Now here in the solution. Let us assume Let's set a Have elements that is one two three right Set b have elements. Let's say one two because few of the elements are common in a and b and let it be four five and Set c may be having elements which are present in a also and some elements are present in b also So let it be one two four and let's say six seven right now Here with the help of an example which I have taken that clearly suggest that set that there is the intersection between Set a and b is equal to the intersection between Set a and set c that is the elements one and two and here also one and two These are the common elements of these three sets But it clearly says that it does not imply Therefore we can write that it does not imply that Set b is equal to set c So it implies that That b is equal to c. So therefore Set b is not equal to set c Right. So this is the Thing that we were supposed to prove in the question that says and we can write down that hence We have shown the required Thing so I hope you understand the question understood it more clearly with the help of a vane diagram Try to take more and more examples to make your thoughts more clear. Bye for now