CSCI 301 L07 Notes

Lecture 7 - Notes

Logic 3

Announcements

Biconditional Statements

Biconditional - “\(P\) if and only if \(Q\)”: \(P \Leftrightarrow Q\)

This means \(P \Rightarrow Q\) and \(Q \Rightarrow P\) are both true.

Do exercises Part A

Do exercises Part B

Equivalences

You can check whether two statements are equivalent by seeing if their truth tables match exactly.

Example: Does \(\land\) distribute over \(\lor\)? In other words

\(A \land (B \lor C) \stackrel{?}{\equiv} (A \land B) \lor (A \land C)\)

Do Exercises Part C

Quantifiers

\(\forall x\) means “for all, or”for every”, or “for each”

\(\exists\) means “there exists a” or “there is a”

Example: For every integer \(x\), \(2x\) is also an integer. Symbolically, \(\forall x \in \mathbb{Z}, 2x \in \mathbb{Z}\).

Example: There is an integer that is even. Symbolically, \(\exists x \in \mathbb{Z}\) such that \(x\) is even.