Questions: Write the statement in symbolic form. Let p and q represent the following statements. p : The dog is very big. q : The dog's bark is loud. It is false that the dog is very big or the dog's bark is loud. Choose the correct answer below. A. ~p ∨ q B. -(p ∧ q) C. -(p ∧ -q) D. -(p ∨ q)

Solution Steps

To express the given statement in symbolic form, we need to translate the English sentence into logical symbols. The statement "It is false that the dog is very big or the dog's bark is loud" can be represented as the negation of the disjunction of \( p \) and \( q \). Therefore, the correct symbolic form is the negation of \( p \vee q \).

We are given two statements:

• \( p \): The dog is very big.
• \( q \): The dog's bark is loud.

The problem asks us to express the statement "It is false that the dog is very big or the dog's bark is loud" in symbolic form.

The phrase "It is false that" indicates a negation. The statement "the dog is very big or the dog's bark is loud" can be represented as \( p \vee q \). Therefore, the entire statement becomes the negation of this disjunction: \( \sim (p \vee q) \).

The symbolic form \( \sim (p \vee q) \) corresponds to option D in the given choices.

Final Answer