Decide, among following sets, which sets are subsets of one and another: A = { x:x ∈ R and x

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1.Set Theory

easy

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

$A = \{ x:x \in R$ and $x$ satisfy ${x^2} - 8x + 12 = 0 \} ,$

$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$

Option A

Option B

Option C

Option D

Solution

$A = \{ x:x \in R$ and $x$ satisfy ${x^2} – 8x + 12 = 0\} $

$2$ and $6$ are the only solutions of $x^{2}-8 x+12=0.$

$\therefore A=\{2,6\}$

$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$

$\therefore D \subset A \subset B \subset C$

Hence, $A \subset B, A \subset C, B \subset C, D \subset A, D \subset B, D \subset C$

Standard 11

Mathematics

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