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Consider the following statements in respect of two non-empty sets A and B :1. A ? B = A ? B if A = B2. A ? B = ? if A = BWhich of the above statements is/are correct ?
Concept:1). A ? B is the symmetric difference that represents the objects that belong to A or B but not to their intersection. A ? B = (A ? B) - (A ? B)2). A ? B subset A is a subset of B. set A is included in set B.3). A ? B, ? is a union, that represents the objects that belong to set A or set B4). A ? B, ? is an intersection, that represents the objects that belong to set A and set B5). a ? A means x is an element of A, i.e. belongs to set membershipCalculation:Given that, A and B are two non-empty sets.Statement I: A ? B = A ? B if A = BLet x ? A ? x ? A ? B, [Because A ? A ? B]? x ? A ? B, [As A ? B = A ? B]? x ? A and x ? B ? x ? A,? B ? ANow, A ? B, B ? A ? A = BStatement I is correct.Statement II: A ? B = ? if A = B? A ? B = ?We know that, A ? B = (A ? B) - (A ? B)? (A ? B) - (A ? B) = ? ? (A ? B) = (A ? B)? A = BStatement II is correct.? Statement I and II both are correct.
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