Question

(c) Determine whether the statement is true or false. Justify your answer.
For all sets A, B and C, if A CB, then An CBnc.
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Answer 1

SOLUTION

TO DETERMINE

Whether the statement is true or false. Justify your answer.

For all sets A, B and C,

If A ⊂ B, then A ∩ C ⊂ B ∩ C

EVALUATION

Here the given three sets are A , B , C

Let x ∈ A ∩ C

⇒ x ∈ A ∧ x ∈ C

⇒ x ∈ B ∧ x ∈ C ( ∵ A ⊂ B gives x ∈ A implies x ∈ B )

⇒ x ∈ B ∩ C

∴ A ∩ C ⊂ B ∩ C

Hence the statement is TRUE

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