Subjective Type

The sets A = {4. 5, 6} and B = {$$x$$ : $$x^2 - 5x - 6 = 0$$} disjoint. Enter 1 if true, or 0 if false.

Solution

Disjoint sets do not have any element in common. Now, $$ {x}^{2} - 5x -6 = 0 $$ $$\Rightarrow {x}^{2} -6x + x - 6 = 0 $$ $$\Rightarrow x(x-6) + (x-6) = 0 $$ $$\Rightarrow (x-6)(x+1) = 0 $$ $$\Rightarrow x = 6, -1 $$ Since $$ 6 $$ in an element in both $$ A $$ and $$ B $$, the sets are not disjoint.

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