Let  A = {a ,b, c , d}, B = {b , d , e ,h}, then  A⊕B  = { a , c , h}Group startsTrue or FalseTrue, unselectedFalse

To determine whether the statement $A \oplus B = \{ a, c, h \}$ is true or false, we first need to understand the operation represented by $\oplus$ in this context. The operation typically represents the symmetric difference of two sets, which includes elements that are in either of the sets but not in their intersection.

1. ### Break Down the Problem

We have two sets:

• $A = \{ a, b, c, d \}$
• $B = \{ b, d, e, h \}$

We need to compute $A \oplus B$, which is defined as: $A \oplus B = (A - B) \cup (B - A)$

2. ### Relevant Concepts

• Set Difference:

  • $A - B$ is the set of elements that are in $A$ but not in $B$.
  • $B - A$ is the set of elements that are in $B$ but not in $A$.

• Union of Sets: The union of two sets is the set that contains all elements from both sets without duplicates.

3. ### Analysis and Detail

1. Calculate $A - B$:

   • $A - B = \{ a, b, c, d \} - \{ b, d, e, h \} = \{ a, c \}$

2. Calculate $B - A$:

   • $B - A = \{ b, d, e, h \} - \{ a, b, c, d \} = \{ e, h \}$

3. Calculate the symmetric difference:

   • Now, combine the results: $A \oplus B = (A - B) \cup (B - A) = \{ a, c \} \cup \{ e, h \} = \{ a, c, e, h \}$

4. ### Verify and Summarize

We found that: $A \oplus B = \{ a, c, e, h \}$ The statement $A \oplus B = \{ a, c, h \}$ is incorrect since we also have element $e$.

Final Answer

The statement is False.