arning Target O1: I can use propositional variables and logical connectives to represent stat symbolic logical statements in plain language. Let p, q and r be the propositions: p: The sun is shining. q: Cats are purring. r: It's time for a nap. 1. Translate the following English sentences into symbolic logic expressions: (a) If cats are purring, then it's not time for a nap. (b) The sun is shining and cats are purring. 2. Translate the following into clear English sentences: (a) (na)

Proficiency #4. [Propositional Logic] Rewrite each of the following statements using only the AND and NOT connectives. (a) PV¬Q (b) (P V Q) → R

Learning Target L1 (Core): I can write the negation, converse, and contrapositive of a conditional statement and use DeMorgan's Laws to simplify symbolic logical expressions. Directions for each of the questions below: If the original statement is in symbols, your answers should be in symbols; if it is in words, the answer should be in clear English as well. For symbolic statements, don't just put in front of the original to form the negation-use De Morgan's laws to simplify. Similarly, for English statements, do no just write "It is not that case that"... to form the negation. 1. For each of the conditional statements below, write the converse, inverse, contrapositive, and negation (fully simplified and clear). (a) If you put gochujang on everything, you are an enlightened person. (b) (p^q) →r) 2. Use De Morgan's laws to state the negations of each of the following (fully simplified and clear): (a) (p^g) Vr) (b) You love spicy food and put gochujang on everything you eat, or you eat…

3. Let us consider the propositional language where: A = "Peter does his homework" B = "Burt does his homework" C = "Andy does his homework" D = "Dexter comes to the party" Write the statement for the following symbols. (d) C → (~D → ~A) (e) (~D → C) A (D → ~B) (f) A A~BAC → ~D) a ( A a B → (D → C)