Prof. X has two brilliant students Yand Zin his class. He introduces theconcept of vector spaces, bases and dimension in his $5$th session. As an exercise,he gives a vector space Vof dimension nand asks Yand Zto find a basis. Yproduces a set Swith nelements. But Zbeing lazy, takes the set S$,$ removesa vector and adds a new vector to it creating a new set T$.$ Prof. X looks at setTand confirms to class that it is a basis. He then asks the class if the set Sproduced by Ycould be a basis without telling them what it is$.$ While studentUsays yes, student Wsays need not and Prof. X says that both U and Wcould be correct. Justify the statement of Prof. X with suitable examples of Vover F$,$n$,$Sand T$.$