Practice and Review 1

Date and Time: Thursday, May 25 at 9:30 am

• Zoom Link
• Recording Link (Passcode: ik@q.u7u) (Zoom Crashed in the last part of the review session, so the end got cut off unfortunately. :( )

Problems

Practice With Quantifiers: Coin Purses

For these problems, let:

• \(S\) be the set of all coins I possess. It could potentially contain any coin type from any country of the world.
• \(C\) be the set of coin purses (Coins go IN these)
• Let \(p(x)\) be a predicate: \(\forall x \in S\), \(p(x)\) is True \(\leftrightarrow x\) is a penny.
• Let \(e(x)\) be a predicate: \(\forall x \in S\), \(e(x)\) is True \(\leftrightarrow x\) is a euro.
• Let \(IN(x,c)\) be a predicate: \(\forall x \in S, \forall c \in C\), \(In(x,c)\) is True \(\leftrightarrow\) coin \(x\) is in coin purse \(c\).
• Let \(q(c)\) be a function that returns the number of coins in coin purse \(c\).

Express the following using predicate logic:

1. No penny is a euro.
2. There are coin purses of different sizes.
3. There is a coin purse for every coin.
4. No coin is without a coin purse. (Extra question: can there be an empty coin purse?)
5. A coin purse with a euro must contain two coins.
6. No coin purse holds both pennies and euros.

Time permitting, we will also review problems from the lessons, but I encourage you to use office hours for this as well!