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