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Are the sets A = {4, 5, 6} and B = {x : x2 – 5x – 6 = 0} disjoint? - Mathematics

Sum

Are the sets A = {4, 5, 6} and B = {x : x2 – 5x – 6 = 0} disjoint?

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Solution

A = {4, 5, 6} 

B = {x : x2 - 5x - 6 = 0}

x2 - 5x - 6 = 0

⇒ x2 - 6x + x -6 = 0

⇒ x(x - 6) +1(x - 6) = 0

⇒ (x - 6) (x+1) = 0

∴ Either x - 6 = 0x

⇒ x = 6

Or 

x+1 = 0

⇒ x = -1

∴ B = {6, -1}

Hence set A and set B are not disjoint because these sets have element 6 in common.

Concept: Types of Sets
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 6 Sets
Exercise 6 (B) | Q 6.1 | Page 67
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