Question

1. let

p: the popcorn is salty.
q: the coffee is creamy.
what are the following statements in symbolic form?
3e \it is false that the popcorn is salty or the coffee is creamy.\
options:
a ( sim (p vee q) )
b ( p vee sim q )
c ( sim p rightarrow q )
d ( sim p wedge q )
3f \it is false that if the coffee is not creamy, then the popcorn is salty.\
options:
a ( sim (p vee q) )
b ( sim (p rightarrow q) )
c ( sim p leftrightarrow q )
d ( sim (sim q rightarrow p) )

Explanation:

Step1: Identify the components

Let \( p \): The popcorn is salty, \( q \): The coffee is creamy. The statement is "It is false that if the coffee is not creamy, then the popcorn is salty." "The coffee is not creamy" is \( \sim q \), and "if the coffee is not creamy, then the popcorn is salty" is \( \sim q \Rightarrow p \).

Step2: Apply negation

Saying "it is false that..." means we negate the entire conditional statement \( \sim q \Rightarrow p \). So the symbolic form is \( \sim (\sim q \Rightarrow p) \).

Answer:

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