Chapter 1: Sets

Exercise

Question

Question: 1

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Decide, among the following sets, which sets are subsets of one and another:

A = {x : x ∈ R and x satisfies x^2 - 8x + 12 = 0}, B = {2, 4, 6}, C = {2, 4, 6, 8, ...}, D = {6}.

Answer

1
Find the elements of the set A by solving the equation (x^2 - 8x + 12 = 0).
x$^2$ - 8x + 12 = 0
(x - 2)(x - 6) = 0
x = 2, 6
Therefore, A = {2, 6}
2
Determine which sets are subsets of others by comparing their elements.
Answer: A $⊂$ B, A $⊂$ C, B $⊂$ C, D $⊂$ A, D $⊂$ B, D $⊂$ C
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