MATHWITHCYE • Discrete Mathematics

Operations on Sets (Operasi Set)

Intersection, union, complement of sets, shading regions on Venn diagrams, and survey problem solving.

1

Intersection of Sets ($\cap$)

The set of elements that belong to BOTH set $A$ and set $B$:

$$A \cap B = \{x : x \in A \text{ and } x \in B\}$$

If $A \cap B = \emptyset$, sets $A$ and $B$ are mutually exclusive / disjoint.

2

Union of Sets ($\cup$)

The set of elements that belong to EITHER set $A$, set $B$, or both:

$$A \cup B = \{x : x \in A \text{ or } x \in B\}$$

Cardinality rule: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.

3

Complement of Sets ($A'$)

The elements in the universal set $\xi$ that do NOT belong to $A$:

$$A' = \{x : x \in \xi \text{ and } x \notin A\}$$

De Morgan: $(A \cup B)' = A' \cap B'$ and $(A \cap B)' = A' \cup B'$.

SPM Shading Technique: The Numbering Method

Never guess which regions to shade in SPM Paper 2! Label each distinct region with a roman numeral or digit (1, 2, 3, 4, ...). Write the regions belonging to each set, and then take their intersection or union before shading. This guarantees you score full marks without silly mistakes!