Question:
For all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C
Solution:
True
According to the question,
There are three sets A, B and C
To check: if A ⊂ B, then A ∪ C ⊂ B ∪ C is true or false
Let x ∈ A ∪ C
⇒ x ∈ A or x ∈ C
⇒ x ∈ B or x ∈ C {∵ A ⊂ B}
⇒ x ∈ B ∪ C
⇒ A ∪ C ⊂ B ∪ C
Hence, the given statement “for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C” is true
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