Propositional Logic

Propositional logic is a branch of logic that deals with propositions. A proposition is a statement like “John is tall”, something that can either be true or false. Propositional logic lets us represent statements like this as letters, e.g. p and work with them and relate them to other statements using logical operators and relations.

Six-minute video

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Key Points

  • Propositions are statements that are either true or false
  • A proposition is called atomic if its truth or falsity is not dependant on any other proposition. For example, Mary is tall
  • A compound proposition does depend on other propositions for truth or falsity. For example Mary is not tall, which is composed of the atomic proposition Mary is tall along with negation.
  • Negation (written ¬) is a logical operation that flips truth values. The negation of a true proposition is false, and vice-versa.

Questions

1. Check your understanding

1. Truth Values

Which propositions are equivalent to TRUE and which are equivalent to FALSE?

  Expression True False  
1.
2.
3.
4.

Check Answers

2. Atomic and Compound Propositions

Identify which of the following are atomic propositions and which are compound propositions:

  Expression Atomic Compound  
1.
2.
3.
4.
5.
6.

Check Answers

3. Negation

Calculate the truth values for the following:

  Expression True False  
1.
2.
3.
4.
5.
6.

Check Answers

4. Double Negation

Complete the following table with either T or F.

p ¬p ¬¬p ¬¬¬p
T
F

Check Answers

2. On paper

Give the negated form of each of the following:

  1. FT212 is on the 2nd floor
  2. David’s office is warm
  3. n < y
  4. my shoes fit my feet

Summary

In this section we have learned about propositional logic.

  • You should be able to assign truth values to propositions and their negations.
  • You should be able to identify atomic and compound propositions.

In the next section we will find out about conjunction and disjunction in propositional logic.