Question
Part 1 I have to use symbols in my anwser Suppose B is proper subset of C If n(c)=8, what is the maxium number of elements in n(B) What is the least possible numbers of Elements in B? Part 2 Suppose C is a subset of D and D is a subset of C If n (C)=5, find n (D) What is other relationship exists between sets C and D? Part 1 I have to use symbols in my anwser Suppose B is proper subset of C If n(c)=8, what is the maxium number of elements in n(B) What is the least possible numbers of Elements in B? Part 2 Suppose C is a subset of D and D is a subset of C If n (C)=5, find n (D) What is other relationship exists between sets C and D?
Explanation / Answer
if all the elements of B are the elements of C and if Bhas atleast one element less than those of C , then we call B is aproper subset of C. now, given C has 8 elements and B is the proper subset of Cmeans B must have a maximum number of 7 elements and all the 7element s must be in C. in set theory, to show to sets C , D are equal , theprocedure we follow is " C is a subset of D and D is a subset ofC"' keeping this in view, given C is a subset of D and D is asubset of C. so, it follows that C = D . since n(C) = 5 , we get n(D) = 5. the other relation ship that exists between C and D is C =D.