Math Snap

STEP 1

Assumptions1. $A=\{a, b, c\}$ is a set. $B=\{b, c, d\}$ is a set3. The union of two sets, denoted $A \cup B$, is the set of elements which are in $A$, in $B$, or in both $A$ and $B$

STEP 2

The union of two sets is defined as the set of elements which are in either of the sets or in both. This means that if an element appears in both sets, it is not repeated in the union of the sets.
$$A \cup B = \{x x \in A \text{ or } x \in B\}$$

STEP 3

Now, let's find the union of the given sets $A$ and $B$.
$$A \cup B = \{a, b, c\} \cup \{b, c, d\}$$

STEP 4

We can see that the elements $b$ and $c$ are in both sets. However, in the union of the sets, each element is listed only once.
$$A \cup B = \{a, b, c, d\}$$

So, it is not true that $A \cup B=\{a, b, c, b, c, d\}$ because in the union of two sets, elements are not repeated. Therefore, the correct answer isA. It is not true that $A \cup B=\{a, b, c, b, c, d\}$ because $A \cup B=\{a, b, c, d\}$. Elements are not repeated in sets.