Q1. Decide, among the following sets, which sets are subsets of one and another:

A = { x : x \in R and x satisfy x^{2} – 8x + 12 = 0 }, B = { 2, 4, 6 },

C = { 2, 4, 6, 8, . . . }, D = { 6 }.

Answers (1)

Solution of this equation are x^{2} – 8x + 12 = 0

                                             ( x - 2 ) ( x - 6 ) = 0

                                                   X = 2,6

                                         \therefore  A = { 2,6 }

                                              B = { 2, 4, 6 }

                                              C = { 2, 4, 6, 8, . . . }

                                               D = { 6 }

From the sets given above, we can conclude that  A \subset B, A \subset C, D \subset A, D \subset B, D \subset C, B \subset C

   Hence, we can say that D \subset A \subset B \subset C

                                               

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