Question

1. let

p: the popcorn is salty.
q: the coffee is creamy.
what are the following statements in symbolic form?
3a \the coffee is not creamy if and only if the popcorn is salty.\
the correct option was a
~ q ⇔ p a
~ p ⇒ q b
p ⇒ ~ q c
~ p ∧ q d
...
5 well done!
3b \if the popcorn is salty, then the coffee is not creamy.\
~ p ⇔ ~ q a
p ⇒ ~ q b
~ p ⇒ ~ q c
p ∧ q d

Explanation:

Step1: Analyze the statement

The statement is "If the popcorn is salty, then the coffee is not creamy." Let \( p \) represent "The popcorn is salty" and \( q \) represent "The coffee is creamy". So "the coffee is not creamy" is \( \sim q \).

Step2: Translate to symbolic form

The "if...then..." structure in logic is represented by the implication symbol \( \Rightarrow \). So "If \( p \), then \( \sim q \)" translates to \( p \Rightarrow \sim q \).

Answer:

B. \( p \Rightarrow \sim q \)