Question

1. let

p: the popcorn is salty.
q: the coffee is creamy.
what are the following statements in symbolic form?
3c \the popcorn is not salty, but the coffee is creamy.\
options:
a ~ p ∧ ~ q
b ~ p ⇒ q
c ~ p ∧ q
d p ⇔ ~ q
3d
either is the popcorn salty nor is the coffee creamy.\
options:
a p ⇔ q
b p ∧ q
c ~ p ∧ ~ q
d ~ q ⇔ ~ p

Explanation:

3d Solution:

Step1: Analyze "Neither...nor..."

"Neither is the popcorn salty nor is the coffee creamy" means the popcorn is not salty (\(\sim p\)) AND the coffee is not creamy (\(\sim q\)).

Step2: Translate to Symbolic Form

The logical connective for "and" is \(\land\), so the statement is \(\sim p \land \sim q\).

Answer:

C. \(\sim p \land \sim q\)