If A \ (B \ C) is simplified, which form is correct?
Answer and explanation
Correct answer: (A \ B) ∪ (A ∩ C)
An element x belongs to A \ (B \ C) when x is in A but not in B \ C. Not being in B \ C means that x is either not in B or is in C. Thus x must satisfy (x ∈ A and x ∉ B) or (x ∈ A and x ∈ C), which gives (A \ B) ∪ (A ∩ C). The identity follows directly from the definition of difference.
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What is the correct answer to this question?
(A \ B) ∪ (A ∩ C)
Why is this the correct answer?
An element x belongs to A \ (B \ C) when x is in A but not in B \ C. Not being in B \ C means that x is either not in B or is in C. Thus x must satisfy (x ∈ A and x ∉ B) or (x ∈ A and x ∈ C), which gives (A \ B) ∪ (A ∩ C). The identity follows directly from the definition of difference.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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