Mini-Quiz May 18

--- tags: 225-spr22, mth225, lt-quiz --- # Mini-Quiz May 18 :::info This is a **mini-quiz**, designed to give you an attempt at **one Learning Target** of your choice from among the more recent ones we've covered, done **quickly** and **in class**. This mini-quiz contains problems for **Learning Targets 3, 5 and 6**. You may attempt Learning Target 3 and **exactly one** of Learning Targets 5 or 6. You may not do both Learning Targets 5 *and* 6 (because this is a "mini" quiz). Work the problems you select out on paper or in a notes app, export the work to PDF (one PDF per Learning Target) and upload it to the appropriate assignment folder on Blackboard just as in the case of a full Quiz. **Your work is due by 2:30pm.** No submissions will be accepted after that time. ::: ## Learning Target 3 :::warning (**CORE**) Given a conditional statement, I can state its hypothesis, conclusion, negation, converse, inverse, and contrapositive. ::: Consider the conditional statement: *If the user enters a wrong number, then an error message appears.* 1. State the **hypothesis** of this statement. 2. State the **conclusion** of this statement. 3. State the **converse** of this statement. 4. State the **inverse** of this statement. 5. State the **contrapositive** of this statement. 6. State the **negation** of this statement (without simply putting "Not" or "It is not the case that" in the front of the statement). **Success criteria:** All answers are given in clear and correct English (*not* in symbolic notation). The negation and contrapositive must be correct, and no more than one error is allowed in the others. --- :::danger Remember: Do **only one** of the following two Learning Targets. ::: ## :new: Learning Target 5 :::warning I can use a truth table to decide if a statement is a tautology or contradiction, or to determine if two statements are logically equivalent. ::: 1. Use truth tables to determine whether the statements $p \rightarrow (\neg q)$ and $(\neg q) \rightarrow (\neg p)$ are logically equivalent or not. 2. Use a truth table to determine whether the statement $(p \wedge q) \rightarrow (p \vee q)$ is a tautology. **Success criteria:** All truth tables have the correct number of rows with no duplicated rows. All intermediate columns are shown. No more than three total errors are permitted. (If you make a mistake in an intermediate column but the rest of the row is correct given that mistake, then the mistake only counts once.) The answers (about whether the statement is a tautology, and about whether the two statements are logically equivalent) are clearly indicated. ## :new: Learning Target 6 :::warning I can determine the truth value of a predicate at a specific input, and given a quantified predicate I can state its negation and its truth value. ::: Consider the predicates: - $P(x)$: $x^2$ is odd - $Q(x)$: The tens digit of $x$ is even The domain of each predicate is the set of all *positive* integers. 1. For each of the following, state whether the expression is **True**, **False**, or **Undetermined**. (a) $P(121)$ (b) $Q(121)$ (c) $\exists x P(x)$ (d) $\exists y (\neg P(x))$ (e) $\forall z Q(z)$ 2. State the negation of the following without just inserting "Not" or "it is not the case that": (a) $\exists x Q(x)$ (b) Every square is a rectangle. (c) Some triangles are equilateral. **Success criteria:** All the answers in the first item are correct. At least two of the three partsof the second item are correct.