Discrete Math - Chapter 1

What is a proposition?

A declarative statement that is either true or false.

Give an example of a proposition.

"The sky is blue." or "The moon is made of cheese."

What type of statements are not propositions?

Commands or statements with variables.

What does the negation of a proposition do?

It reverses the truth value of the proposition.

What symbol represents negation?

¬ or 'not'.

What is the truth value of ¬P if P is true?

False.

What is the truth value of ¬P if P is false?

True.

What does a conjunction (P ∧ Q) mean?

It means 'P AND Q' are both true.

When is P ∧ Q true?

Only when both P and Q are true.

What symbol represents conjunction?

∧.

What does a disjunction (P ∨ Q) mean?

It means 'P OR Q' (inclusive OR).

When is P ∨ Q false?

Only when both P and Q are false.

What is the difference between inclusive and exclusive OR?

Inclusive OR allows both to be true; exclusive OR does not.

What symbol is used for exclusive OR?

⊕.

When is P ⊕ Q true?

When exactly one of P or Q is true.

How many rows are in the truth table for two propositions?

Four.

For n propositions, how many rows does a truth table have?

2^n

Give an example of an inclusive OR statement.

"You can take MA 315 or MA 335 to enroll in MA 420."

Give an example of an exclusive OR statement.

"You get soup or salad with your entrée (but not both)."

What do propositions in discrete math usually get named with?

Lowercase letters like p