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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» 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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