For all sets A, B and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C

Question

Determine whether statement are true or false. Justify your answer.

For all sets A, B and C, if A ⊂ B, then A ∩ C ⊂ B ∩ C

Answer 1

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.