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For all sets A, B and C,

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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