The proposition “The night is dark and full of terrors” is a substitution instan

Question

The proposition “The night is dark and full of terrors” is a substitution instance of which of the following propositional forms? (Select all that apply)

p q

Is the following argument valid by virtue of its propositional form?

“Tom owns a house. Therefore, Tom owns a house and a piece of land.”

No, the argument is invalid in virtue of its propositional form.

Given that "A", "B", and "C" are true propositions, and "X", "Y", and "Z" are false propositions, determine the truth value of the following compound proposition.

~~(A B)

False

Given that "A", "B", and "C" are true propositions, and "X", "Y", and "Z" are false propositions, determine the truth value of the following compound proposition.

~Z (Z & A)

Explanation / Answer

1. The night is dark and full of terrors

Let p: The night is dark, q: The night is full of terrors

The given statement translates to p & q.

2. "Tom owns a house. Therefore, Tom owns a house and a piece of land."

Let p: Tom owns a house and q: Tom owns a piece of land.

The given statement translates to p -> (p & q)

If p is true and q is false then p -> (p & q) is true -> false which is false.

No. The argument is not valid in virtue of it's propositional form.

3. A and B are true

=> A V B is true

~~(A B) is true by rule of double negation.

4. A is true and Z is false

=> (Z & A) is false, ~Z is true

=> ~Z (Z & A) is true.

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