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# Which of the following sets are empty, singleton, pair and which of them are equal.  A = {x : $x^2$ = 9 and 2x = 3}  B = {x : $x^2$ – 5x + 6 = 0, 2x = 6}  C = {x : $x^2$ – 4x + 3 = 0}  D = {x : $x^2$ = 25}  E = {x : 2x = 6 or x = 1}

A = {x : $x^2$ = 9 and 2x = 3} = {x : (x = 3 or x = –3} and x = $\large\frac{3}{2}$ }
No x satisfies both the conditions. So there is no x in A i.e., A = $\phi$
B = {x : $x^2$ – 5x + 6 = 0, 2x = 6}
= {x : (x – 3) (x – 2) = 0, x = 3}
= {x : (x = 3 or x = 2) = 0 and x = 3}
Only x = 3 satisfies both the predicates. So x has only one value 3.
$\therefore$ B = {3}
C = {x : $x^2$ – 4x + 3 = 0}
= {x : (x – 3) (x – 1) = 0}
= {x : x = 3 or x = 1}
2 and 1 both satisfy the statement x = 3 or x = 1
$\therefore$ C = {1 , 3}
Similarly, D = {-5, 5} and E = {1, 3}
Thus A is an empty set; B is a singleton set; C, D, E is pair sets.
Also, C = E