Given $U = \{1, 2, \ldots, 15\}$, $A = \{1, 2, 3, 5, 15\}$, $B = \{2, 4, 6, 8, 10, 12, 14\}$, $C = \{2, 3, 5, 7, 11, 13\}$. $C - B =$

(a) $\{3, 5, 7, 13\}$
(b) $\{3, 5, 7, 2, 13\}$
(c) $\{3, 5, 7, 11, 13\}$
(d) $\phi$

Well-defined: For any object, we can say yes or no — no ambiguity.
Distinct: No duplicates — each object appears only once.

Question

Given $U = \{1, 2, \ldots, 15\}$, $A = \{1, 2, 3, 5, 15\}$, $B = \{2, 4, 6, 8, 10, 12, 14\}$, $C = \{2, 3, 5, 7, 11, 13\}$. $C - B =$

(a) $\{3, 5, 7, 13\}$
(b) $\{3, 5, 7, 2, 13\}$
(c) $\{3, 5, 7, 11, 13\}$
(d) $\phi$

Accepted Answer

>

> [!TLDR]
> $C - B = \{3, 5, 7, 11, 13\}$.
>
> Given $C = \{2, 3, 5, 7, 11, 13\}$ and $B = \{2, 4, 6, 8, 10, 12, 14\}$.
> …

Property	Statement
Not commutative	$A - B \neq B - A$ in general
Difference with itself	$A - A = \emptyset$
Difference with empty set	$A - \emptyset = A$ , and $\emptyset - A = \emptyset$
Difference with universal set	$U - A = A^c$ (the complement of $A$ )
Disjoint sets	If $A \cap B = \emptyset$ , then $A - B = A$

Q.Given $U = \{1, 2, \ldots, 15\}$ , $A = \{1, 2, 3, 5, 15\}$ , $B = \{2, 4, 6, 8, 10, 12, 14\}$ , $C = \{2, 3, 5, 7, 11, 13\}$ . $C - B =$