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

To determine if the statement A⊕B = {a, c, h} is true or false, we first need to understand what the operation A⊕B refers to in the context of sets. The symbol ⊕ typically denotes the symmetric difference between two sets. The symmetric difference of two sets A and B, denoted A⊕B, is defined as the set of elements that are in either of the sets, but not in their intersection.

Step 1: Identify the Elements of Each Set

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

Step 2: Determine the Intersection of A and B

The intersection of A and B (A ∩ B) includes elements common to both sets:

• A ∩ B = {b, d}

Step 3: Calculate the Symmetric Difference A⊕B

The symmetric difference A⊕B is obtained as follows: $A \oplus B = (A \cup B) - (A \cap B)$

• First, find the union of A and B: $A \cup B = \{a, b, c, d\} \cup \{b, d, e, h\} = \{a, b, c, d, e, h\}$
• Remove the elements in the intersection: $A \oplus B = \{a, b, c, d, e, h\} - \{b, d\} = \{a, c, e, h\}$

Step 4: Verify the Result

Now we compare the result of A⊕B with the given set {a, c, h}. The calculated symmetric difference was {a, c, e, h}, which includes an extra element 'e'.

Final Answer

The statement A⊕B = {a, c, h} is False. The correct answer is A⊕B = {a, c, e, h}.