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Home » Determine whether each of the statement in Exercise For all sets A and B, (A – B) ∪ (A ∩ B) = A is true or false. Justify your answer.
Determine whether each of the statement in Exercise For all sets A and B, (A – B) ∪ (A ∩ B) = A is true or false. Justify your answer.
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
Determine whether each of the statement in Exercise For all sets A and B, (A – B) ∪ (A ∩ B) = A is true or false. Justify your answer.

Solution:

The statement is true

As per the question,

Two sets A and B

We need to check: (A-B) \cup(A \cap B)=A is true or false

Left Hand Side =(A-B) \cup(A \cap B)

As, A-B=A \cap B' ,

We have,

=\left(A \cap B^{\prime}\right) \cup(A \cap B)

By the distributive property of set:

We have,

\begin{array}{l} (A \cap B) \cup(A \cap C)=A \cap(B \cup C) \\ =A \cap\left(B^{\prime} \cup B\right) \\ =A \cap U \\ =A \\ =\text { Right Hand Side } \end{array}

As a result, the given statement “for all sets A and B, (A-B) \cup(A \cap B)=A^{\prime \prime} is true.

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