Let A1, A2 and A3 be subsets of a set X. Which one of the following is correct?

Question

Let A1, A2 and A3 be subsets of a set X. Which one of the following is correct? (A) A1 ∪ A2 ∪ A3 is the smallest subset of X containing elements of each of A1, A2 and A3 (B) A 1 ∪ A 2 ∪ A 3 is the smallest subset of X containing either A 1 or A 2 ∪ A 3 but not both (C) The smallest subset of X containing A1 ∪ A2 and A3 equals the smallest subset of X containing both A1 and A2 ∪ A3 only if A2=A3 (D) None of these

Tardigrade Admin · Accepted Answer

A1 ∪ A2 ∪ A3 is the smallest element containing subset of all we set A1, A2 and A3

Q. Let $A_{1}, A_{2}$ and $A_{3}$ be subsets of a set $X$ . Which one of the following is correct?

$A_{1} \cup A_{2} \cup A_{3}$ is the smallest subset of $X$ containing elements of each of $A_{1}, A_{2}$ and $A_{3}$

$A_{1} \cup A_{2} \cup A_{3}$ is the smallest subset of $X$ containing either $A_{1}$ or $A_{2} \cup A_{3}$ but not both

The smallest subset of $X$ containing $A_{1} \cup A_{2}$ and $A_{3}$ equals the smallest subset of $X$ containing both $A_{1}$ and $A_{2} \cup A_{3}$ only if $A_{2} = A_{3}$

None of these

$A_{1} \cup A_{2} \cup A_{3}$ is the smallest element containing subset of all we set $A_{1}, A_{2}$ and $A_{3}$

Q. Let A1​,A2​ and A3​ be subsets of a set X. Which one of the following is correct?

A1​∪A2​∪A3​ is the smallest subset of X containing elements of each of A1​,A2​ and A3​

A1​∪A2​∪A3​ is the smallest subset of X containing either A1​ or A2​∪A3​ but not both

The smallest subset of X containing A1​∪A2​ and A3​ equals the smallest subset of X containing both A1​ and A2​∪A3​ only if A2​=A3​