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Asked by Amit Last Modified
Answer As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into the properties of sets to prove the given statement.
To prove: A−(A∩B)=A−BA−(A∩B)=A−B
Let's break it down step by step using set operations:
Left-hand side (LHS) of the equation: A−(A∩B)A−(A∩B)
Right-hand side (RHS) of the equation: A−BA−B
To prove the equality, we need to show that the LHS is equal to the RHS.
Proof:
Let's start with the LHS: A−(A∩B)A−(A∩B)
Now, let's consider the RHS: A−BA−B
If we compare the two operations:
It follows that whatever elements were in both A and B, they are removed in both operations.
Therefore, A−(A∩B)=A−BA−(A∩B)=A−B, proving the equality.
This completes the proof, demonstrating that for all sets A and B, A−(A∩B)A−(A∩B) is indeed equal to A−BA−B. This principle is fundamental in set theory and can be useful in various mathematical and logical contexts.
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