Which of the following sets are equal?

S₁ = {1, 2, 2, 3},

S₂ = {x | x² - 2x + 1 = 0},

S₃ = {1, 2, 3},

S₄ = {x | x³ - 6x² + 11x - 6 = 0},

Ans: The elements of S₂ and S₄ is given like this:

S₂ = {1, 1} and S₄ = {1, 2, 3}

Two sets are said to be equal if both consist of same elements and the multiplicity of each element is similar in both the sets. This implies that S₃ and S₄ are equal. Although S₁ has similar elements as in S₃ and S₄, it not equal as multiplicity of 2 in S₁ is 2 whereas that in S₃ and S₄ is 1