Question

Let A = {2, 3, 4, 5, 6, 7}, B = {2, 4, 7, 8}, C = {2, 4}, then which of the following statements are True?
(a) B $\subset $ A
(b) C $\subset $ A
(c) B $\subseteq $ C
(d) C $\subset $ B
(A) Both (a) and (d)
(B) Both (b) and (d)
(C) Only (d)
(D) Only (b)

Answer 1

Hint: First understand the difference between the symbols $\subset $ and $\subseteq $ that represents proper subset and subset respectively. Now, check the members of all the three sets and see. If all the members of a particular set are present in the other set then the first set is a proper subset of the second set only if the second set contains some elements that are not present in the first set. In the other case if all the members of the two sets are equal then they are subsets of each other but not the proper subset.

Complete step by step answer:
Here we have been provided with three sets A = {2, 3, 4, 5, 6, 7}, B = {2, 4, 7, 8}, C = {2, 4} and we are asked to choose the correct option by finding which set is a subset or a proper subset of the other.
Now, let us understand the difference between a subset and a proper subset. Suppose we have two sets M and N, so the following two cases along with their conclusions arises: -
(1) If all the elements of set M are present in set N and set N does not contain any element that is not present in set M, in other words we have two equal sets (M = N), then in such a case M and N are subsets of each other. It is represented by the symbol $\subseteq $.
(2) If all the elements of set M are present in set N and set N contain some elements that are not present in set M, then in such a case M is a proper subset of N. It is represented by the symbol $\subset $.
Let us come to the question, clearly we can see that all the elements of set C is present in set A and B but set A and B contains some elements that are not present is set C, so set C is a proper subset of set A and B. Therefore, we have C $\subset $ A and C $\subset $ B which means both (b) and (d) are correct.

So, the correct answer is “Option B”.

Note: Note that we do not have any subset relation between sets A and B because set B contains an element 8 which is not present in set A so we have the conclusion B $\not\subset $ A or A $\not\subset $ B. Remember the definitions and symbols of the two terms so that you might not get confused while solving the problems.