Chapter 1: Sets

Exercise

Question

Question: 2 (vi)

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In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(vi) If A ⊂ B and x ∉ B, then x ∉ A

Answer

1
Determine whether the given information is sufficient to always conclude that x is not an element of set A.
Answer: True
2
Prove that if an element does not belong to set B, then it also does not belong to set A.
Proof:
Since A $⊂$ B, every element of set A must also be an element of set B. Therefore, if x is not an element of set B, it cannot be an element of set A. Hence, the given statement is always true.
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