Q1 of 86 Page 26

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

A = {x : x ∈ R and x satisfy x2 – 8x + 12 = 0},


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

It is given in the question that,

A = {x : x R and x satisfy x2 – 8x + 12 = 0}


As, 2 and 6 are the only solutions of x2 – 8x + 12 = 0


∴ A = {2, 6}


Also it is given that,


B = {2, 4, 6}


C = {2, 4, 6, 8, …..}


And, D = {6}


∴


Hence,


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In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example:

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