Question

For which conditions is p ∨ q false?

A)p is true and q is false.
B)p is true and q is true.
C)p is false and q is true.
D)p is false and q is false.

Answer 1

D)p is false and q is false.

Answer 2

D)p is false and q is false.

Explanation:

This is the case of the disjunction operator. This operator creates a compound statement that:

1. It's true if either simple statement is true

2. It's false if both simple statements are false.

So p and q are statements and the only way the compound statement is false is when both simple statements are false. For instance:

For:

p: "Peter is home"

q: "Charles is home"

The disjunction would look like these two forms:

p v q

Other form to write this is as follows:

Peter is home OR Charles is home.

So the compound statement is false if both Peter and Charles aren't home.