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Intermediate ⛓ Discrete Math & Number Theory Topic 2 of 103

Logical Connectives

AND, OR, NOT, implication and biconditional.

Key idea

AND, OR, NOT, implication and biconditional.

In depth

Connectives build compound statements: not (¬), and (∧), or (∨), implies (→), if and only if (↔). The truth of a compound depends only on the truth of its parts. In mathematics, "or" is inclusive.

Worked example

"2 is even and 3 is even" is false, while "2 is even or 3 is even" is true.

Formula

p ∧ q, p ∨ q, ¬p, p → q

Real-world uses

Common mistake

Reading "or" as exclusive; p ∨ q is true when both are true.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Logical Connectives?

AND, OR, NOT, implication and biconditional. It is a topic at the intermediate level in Discrete Math & Number Theory.

What is the formula for Logical Connectives?

The key formula is p ∧ q, p ∨ q, ¬p, p → q.

Where is Logical Connectives used in real life?

Real-world examples: Writing search filters (AND, OR, NOT) and program conditions such as “age ≥ 18 and has ID”.

What should I learn before Logical Connectives?

Make sure you are comfortable with Statements and Truth Values, the previous topic in Discrete Math & Number Theory.

What is a common mistake with Logical Connectives?

Reading "or" as exclusive; p ∨ q is true when both are true.

How can I practise Logical Connectives?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Logical Connectives?

Move on to Truth Tables next.

Related intermediate topics in Discrete Math & Number Theory