Q15 of 58 Page 12

Determine whether each of the statement in

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

Given: 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 is true


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