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InterviewSolution
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Decide among the following sets, which are subsets of which:`A={x : x`satisfies `x^2-8x+12=0}, B={2,4,6}, C={2,4,6,8 }, D={6}dot` |
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Answer» `A={x:x in R and x^(@)-8x+12=0}` `:. x^(2)-8x+12=0 or x^(2)-(2+6)x+12=0` or `x^(2)-2x-6x +12 =0` or `x(x-2) - 6(x-2)=0` or `(x-2)(x-6)=0 rArr x=2,6` `:. A={2,6} and B={2,4,6},C={2,4,6,8,...},D={6}` `:. 6` is an element in all sets and it is one elements of singleton set D `:.D subA,D subB,D subC` `because` In `A = {2,6} and B = {2,4,6}`, each element of A is in B `A sub B` Similarly, in `B = {2,4,6} and C = {2,4,6,8,...}` each element of B and A is in C `A sub C and B sub C` Therefore, `D subB,B subC,A subC,D subA,D subC, A subB`. |
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