Question Bank - Mathematics

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Consider the following statements in respect of two non-empty sets A and B :1. x ? (A ? B) ? x ? A or x ? B2. x ? (A ? B) ? x ? A and x ? BWhich of the above statements is/are correct?

A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2

Solution:

Concept:Complement of set A or A' contains elements other than elements of set A.x ? A means x is not an element of A, i.e. no set membershipa ? A means x is an element of A, i.e. belongs to set membership Calculation:Given that, A and B are two non-empty sets.Statement I: x ? (A ? B) ? x ? A or x ? BAs x ? (A ? B)? x ? (A ? B)'? x ? A' and x ? B'? x ? A and x ? BStatement I is incorrect.Statement II: x ? (A ? B) ? x ? A and x ? BAs x ? (A ? B)x ? (A ? B)'? x ? A' or x ? B'? x ? A or x ? BStatement II is incorrect.? Neither statement I nor II is correct.

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