 I am welcome to the session I am Asha and I am going to help you with the following question which says, Decide among the following sets which sets are subsets of one and another. So first let us learn what are subsets whose symbol is this. So every element of a set suppose A is also an element to set, let us say to B then we say A is a subset of set B and is denoted by A is a subset of B. So this definition is a key idea that we will be using in this problem to solve it. Let us now start with the solution and the set A contains all x such that x belongs to R and x satisfy square minus 8x plus 12 is equal to 0. So we have to find the x which satisfies this equation which is x square minus 8x plus 12 is equal to 0. So on splitting the middle term minus 8x can be written as minus 6x minus 2x then we have plus 12 is equal to 0. Now taking x common from the first two terms and minus 2 common from the next two terms it can be further written as x into x minus 6 minus 2 into x minus 6 is equal to 0. Now taking x minus 6 common we are left with x and minus 2 is equal to 0. So this implies either x minus 6 is equal to 0 or x minus 2 is equal to 0 which further implies x is equal to 6 or x is equal to 2. Thus set A have elements and 6. Also set B as given to us have elements 2, 4 and 6 set C is 2, 4, 6, 8 and so on and set D have only one element but a 6. Now we see that elements of A, elements of B so A is subset of B. All the elements of A are elements of, A is also subset of C. Elements of B are also elements of C. So D is a subset of C. All the elements of D are also elements of A. So D is a subset of A. Also all the elements of D are also elements of set B. So we can say that D is a subset of set B. Lastly the elements of D are again elements of set C. So D is a subset of C and hence we have all these 6 pairs and thus our answer is A is a subset of B first and A is also a subset of C. B is a subset of C, D is a subset of A, D is a subset of B and D is a subset of C. So this completes the solution. Hope you enjoyed it. Take care and have a good day.