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Sets — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSSets3 Marks
Question
Are the sets $A = \{4, 5, 6\}$ and $B = \{x : x^2 – 5x – 6 = 0\}$ disjoint?
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Answer

$A = \{4, 5, 6\}$
$B = \{x : x^2 - 5x - 6 = 0\}$
$x^2 - 5x - 6 = 0$
$\Rightarrow x^2 - 6x + x -6 = 0$
$\Rightarrow x(x - 6) +1(x - 6) = 0$
$\Rightarrow (x - 6) (x+1) = 0$
$\therefore $ Either $x - 6 = 0x$
$\Rightarrow x = 6$ Or $x+1 = 0$
$\Rightarrow x = -1$
$\therefore B = \{6, -1\}$
Hence set $A$ and set $B$ are not disjoint because these sets have element $6$ in common.

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