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### Question

1. State the negation of the following propositions. m: Mathematics is easy to study. m n: Nellie’s favorite song is “Hero” by Mariah Carey. o: Logic is not taken up in junior high school. p:x² – 453 + x q: There are at least three people in the meeting room at the moment. 2. Let p, q, and r be the propositions p: “Rena eats at the Spanish restaurant.”, q: “Rena orders the restaurant’s special paella.”, r: “Rena has dessert.” Express the following statements in English sentences or in symbols, as the case may be. a. “Rena orders the restaurant’s special paella, but she does not have dessert.” b. “Whenever Rena eats at the Spanish restaurant, either she orders the restaurant’s special paella or she has dessert.” c. “If Rena eats at the Spanish restaurant, she orders the restaurant’s special paella if and only if she does not order dessert.” d. p – (91(r)) vr) e. p-((-9) -r) f.((9)^(r)) – (-p) 3. Consider the propositions u: “Pam works as a sales associate.” v: “Bryan has a temporary position in the office.” and w: “Pam and Bryan are co-workers.” Express the following propositions in English sentences or in symbols as the case may be. a. “Pam and Bryan are co-workers, but Pam works as a sales associate and Bryan does not have a temporary position in the office.” b. “Pam and Bryan are co-workers, but if Bryan has a temporary position in the office, then Pam does not work as a sales associate.”

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### Answer #1 for Questions: 1. State the negation of the following propositions. m: Mathematics is easy to study. m n: Nellie’s favorite song is “Hero” by Mariah Carey. o: Logic is not taken up in junior high school. p:x² – 453 + x q: There are at least three people in the meeting room at the moment. 2. Let p, q, and r be the propositions p: “Rena eats at the Spanish restaurant.”, q: “Rena orders the restaurant’s special paella.”, r: “Rena has dessert.” Express the following statements in English sentences or in symbols, as the case may be. a. “Rena orders the restaurant’s special paella, but she does not have dessert.” b. “Whenever Rena eats at the Spanish restaurant, either she orders the restaurant’s special paella or she has dessert.” c. “If Rena eats at the Spanish restaurant, she orders the restaurant’s special paella if and only if she does not order dessert.” d. p – (91(r)) vr) e. p-((-9) -r) f.((9)^(r)) – (-p) 3. Consider the propositions u: “Pam works as a sales associate.” v: “Bryan has a temporary position in the office.” and w: “Pam and Bryan are co-workers.” Express the following propositions in English sentences or in symbols as the case may be. a. “Pam and Bryan are co-workers, but Pam works as a sales associate and Bryan does not have a temporary position in the office.” b. “Pam and Bryan are co-workers, but if Bryan has a temporary position in the office, then Pam does not work as a sales associate.”

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**Answer:**

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