1. Given: p = Jess is 17 years old, q = Mina lives in Pili. and r = Math is easy. Write in
symbols the following propositions:
(a) Jess is not 17 years old.
(b) Either Mina lives in Pili or Math is easy.
(c) Jess is 17 years old and Math isn’t easy.
(d) Mina lives in Pili if and only if Jess is 17 years old.
(e) It is false that Math is easy and Mina lives in Pili.

Let's represent the given propositions using logical symbols:

1. **Given Propositions:**
   - \( p \) : Jess is 17 years old.
   - \( q \) : Mina lives in Pili.
   - \( r \) : Math is easy.

2. **Required Propositions in Symbols:**

   (a) **Jess is not 17 years old.**  
   \[ \neg p \]

   (b) **Either Mina lives in Pili or Math is easy.**  
   \[ q \lor r \]

   (c) **Jess is 17 years old and Math isn’t easy.**  
   \[ p \land \neg r \]

   (d) **Mina lives in Pili if and only if Jess is 17 years old.**  
   \[ q \leftrightarrow p \]

   (e) **It is false that Math is easy and Mina lives in Pili.**  
   \[ \neg (r \land q) \]

Would you like further details on any of these symbolic expressions?

Here are 5 related questions for further exploration:

1. What is the symbolic representation of "If Math is easy, then Jess is 17 years old"?
2. How would you express "Neither Jess is 17 years old nor Mina lives in Pili" using symbols?
3. What does the logical expression \( p \lor \neg q \) mean in words?
4. How would you symbolically represent "Jess is 17 years old or Mina does not live in Pili"?
5. Can you express "It is false that Jess is not 17 years old or Math is easy" using symbols?

**Tip:** When dealing with logical propositions, always pay close attention to the logical connectors (and, or, not, if-then, etc.) as they define the relationship between the statements.

Explore logical propositions involving Jess's age, Mina's residence, and the difficulty of math problems. Learn how to symbolically represent statements about age, residence, and difficulty in logical terms. Suitable for high school students studying propositional logic.

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