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 gym."}}##\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?
If grass is not green, it is brown.
If my fingers become purple, I go to a doctor.
Elephants can fly.
Do you know where the milk or the flour is?
If grass is not green, it is brown.
If my fingers become purple, I go to a doctor.
Elephants can fly.
The propositions "If grass is not green, it is brown" and "If my fingers become purple, I go to a doctor" 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 "Elephants can fly" 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 "Elephants can fly" is a simple proposition.
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