Assignment of Maths for Grade 9 Give the Correct answer 1) A universal.set u=1,2,3, ldots, 14, A=2,3,5,7,11 , B=2,4,8,9,10,11 . Then which one of the following true A) (A cup B)^prime=1,4,6,12,13,14 B) A cap B=A^prime cup B^prime G) A triangle B=(A cap B)^prime D) A mid B=3,5,7 E, none

## Step 1: Determine \( A \cup B \)<br />### The union of sets \( A \) and \( B \), denoted as \( A \cup B \), includes all elements from both sets without duplication. Thus, \( A \cup B = \{2,3,4,5,8,9,10,11\} \).<br />## Step 2: Calculate \( (A \cup B)^{\prime} \)<br />### The complement of \( A \cup B \) with respect to the universal set \( u \) is found by identifying elements in \( u \) that are not in \( A \cup B \). Therefore, \( (A \cup B)^{\prime} = \{1,6,7,12,13,14\} \).<br />## Step 3: Verify Option A<br />### Compare \( (A \cup B)^{\prime} = \{1,6,7,12,13,14\} \) with the given option \( \{1,4,6,12,13,14\} \). They do not match.<br />## Step 4: Determine \( A \cap B \)<br />### The intersection of sets \( A \) and \( B \), denoted as \( A \cap B \), includes only elements common to both sets. Thus, \( A \cap B = \{2\} \).<br />## Step 5: Verify Option B<br />### Check if \( A \cap B = A^{\prime} \cap B^{\prime} \). Since \( A^{\prime} = \{1,4,6,7,8,9,10,11,12,13,14\} \) and \( B^{\prime} = \{1,3,5,6,7,12,13,14\} \), their intersection is \( \{1,6,7,12,13,14\} \), which does not equal \( \{2\} \).<br />## Step 6: Determine \( A \triangle B \)<br />### The symmetric difference \( A \triangle B \) consists of elements in either \( A \) or \( B \) but not in both. Thus, \( A \triangle B = \{3,4,5,8,9,10,11\} \).<br />## Step 7: Verify Option C<br />### Check if \( A \triangle B = (A \cap B)^{\prime} \). Since \( (A \cap B)^{\prime} = \{1,3,4,5,6,7,8,9,10,11,12,13,14\} \), they do not match.<br />## Step 8: Verify Option D<br />### The notation \( A \mid B \) is unclear, but assuming it means a specific operation, verify against \( \{3,5,7\} \). No standard set operation results in this set.