### Logic: Propositional logic

### Compound propositions

Up to this point, we have seen propositions and logical operators. With these two ingredients, we can build compound propositions.

Simple and compound propositions

A proposition is called a **simple** **proposition** if it does not contain any of the logical operators #\neg#, #\lor#, #\land#, #\rightarrow#, and #\leftrightarrow#.

A proposition is called a **compound proposition** if it contains one or more of the logical operators #\neg#, #\lor#, #\land#, #\rightarrow#, and #\leftrightarrow#.

**Examples of simple propositions**

#\blue{\textrm{"I go to the swimming pool."}}#

#\blue{\textrm{"I take a shower."}}#

**Example of a compound proposition**

#\blue{\textit{"If}\textrm{ I go to the gym }\textit{or}\textrm{ the swimming pool,}} #

#\blue{\textit{then}\textrm{ I take a shower."}}#

Select all compound propositions from the options below.

Do you know where the milk or the flour is?

Cars can be blue or black, but not yellow.

I like spicy food, but not when it is cold outside.

Sheep have five legs.

Do you know where the milk or the flour is?

Cars can be blue or black, but not yellow.

I like spicy food, but not when it is cold outside.

Sheep have five legs.

The propositions "Cars can be blue or black, but not yellow" and "I like spicy food, but not when it is cold outside" are compound expressions.

The expression "Do you know where the milk or the flour is?" is not a proposition, and therefore it is not a compound proposition either.

The expression "Sheep have five legs" is a simple proposition.

The expression "Do you know where the milk or the flour is?" is not a proposition, and therefore it is not a compound proposition either.

The expression "Sheep have five legs" is a simple proposition.

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