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Learning Objectives:

Understand notations related to set representation and operations.
Perform the operations of union, intersection, complement, and difference on sets.
Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems.

N = {1, 2, . . .}, the set of Natural numbers;
W = {0,1,2,...}, the set of whole numbers
Z = {0,1,−1,2,−2,...}, the set of Integers;
Q ={$\dfrac{p}{q}$ :p,q∈Z, q $\neq$ 0},the set of Rational numbers;
R = the set of Real numbers; and
C = the set of Complex numbers.
We will use $\phi$ to denote an empty set.

Operations on sets:

Union: Denoted by $\cup$ symbol, such as $A \cup B$.
Intersection: Denoted by $\cap$ symbol, such as $A \cap B$

Solved Example: 121223

If A = {1, 2, 3} and B = {3, 6, 8} then $(A\cap B) \times A$ is:

A. {(1, 3), (2, 3), (3, 3)}

B. {(3, 1), (3, 2), (3, 3)}

C. {(1, 3), (3, 1), (3, 2)}

D. None of these

\begin{align*} (A \cap B) &= \{3\}\\ (A \cap B) \times A &= \{(3,1),(3,2),(3,3)\} \end{align*}

Correct Answer: B

Important Points:

Digraph = Directed graph
It is a diagram composed of points called vertices (nodes) and arrows called arcs going from a vertex to a vertex.

Solved Example: 9960-01

If we want to represent a relation between number of link current and number of branch currents in a directional graph, we should use: (DFCCIL Executive Electrical 2016)

A. Reduced incidence

B. Incidence

C. Tie set

D. Cutset

Correct Answer: C

Discrete Mathematics