Q.Let $U = \{1, 2, 3, \dots, 10\}$, $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7\}$. Find

Apply each operation's definition directly to the listed elements, reading the complement relative to the given universal set $U$.

$A \cup B = \{1,2,3,4,5,6,7\}$; $A \cap B = \{4,5\}$; $A - B = \{1,2,3\}$; $A' = \{6,7,8,9,10\}$.

Work from the definitions of each operation.

(i) Union $A \cup B$ — all elements in $A$ or $B$ (or both), each listed once:

(ii) Intersection $A \cap B$ — elements common to both:

(iii) Difference $A - B$ — elements in $A$ but not in $B$; remove $4$ and $5$ (which are in $B$) from $A$:

(iv) Complement $A'$ — elements of $U = \{1, \dots, 10\}$ not in $A$:

Cross-check using $n(A \cup B) = n(A) + n(B) - n(A \cap B)$: $5 + 4 - 2 = 7$, and indeed $A \cup B$ has $7$ elements.

The most common error is computing the complement against the wrong universal set (or forgetting $U$ altogether); $A'$ has no meaning until $U$ is fixed. A second slip is listing shared elements like $4$ and $5$ twice in the union.