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 and x ∈ C
⇒ x ∈ B and 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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