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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
Similar Questions
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
| $(i)$ $\{ P,R,I,N,C,A,L\} $ | $(a)$ $\{ x:x$ is a positive integer and is adivisor of $18\} $ |
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| $(iv)$ $\{ 3, – 3\} $ | $(d)$ $\{ x:x$ is aletter of the word $PRINCIPAL\} $ |
medium
