Question

Statement I A compound statement with an "or" is true when one component statement is true or both the component statement are true.
Statement II A compound statement with an "or" is false when both the component statements are false.

• A. Statement I is true; Statement II is true; Statement II is a correct explanation for Statement I
• B. Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I
• C. Statement I is true; Statement II is false
• D. Statement I is false; Statement II is true

Answer 1

Answer: (B)

I. A compound statement with an "or" is true when one component statement is true or both the component statements are true.
II. A compound statement with an "or" is false when both the component statements are false.
For example, consider the following statement.
$p$ : two lines intersect at a point or they are parallel.
The component statements are
$q$ : two lines intersect at a point.
$r$ : two lines are parallel.
Then, when $q$ is true, $r$ is false and when $r$ is true, $q$ is false. Therefore, the compound statement $p$ is true.
Consider another statements.
$p:125$ is a multiple of 7 or 8 .
Its component statements are
$q:125$ is a multiple of 7 .
$r:125$ is a multiple of 8
Both $q$ and $r$ are false. Therefore, the compound statement $p$ is false.