Using that for any sets mathrm{A} and mathrm{B}, A cup(A cap B)=A

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1.Set Theory

easy

Using that for any sets $\mathrm{A}$ and $\mathrm{B},$

$A \cup(A \cap B)=A$

Option A

Option B

Option C

Option D

Solution

To show: $A \cup(A \cap B)=A$

We know that

$A \subset A$

$A \cap B \subset A$

$\therefore A \cup(A \cap B) \subset A$ ……….$(1)$

Also, $A \subset A \cup(A \cap B)$ …………..$(2)$

$\therefore$ From $(1)$ and $(2), A \cup(A \cap B)=A$

Standard 11

Mathematics

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