Question

6 multiple choice 1 point given these true statements: “if the negotiations fail, the baseball strike will not end.” “if the world series is played, the baseball strike has ended.” which conclusion logically follows? if the baseball strike ends, the world series will be played. if negotiations fail, the world series will not be played. if negotiations fail, the world series will be played. if negotiations do not fail, the baseball strike will not end. 7 multiple choice 1 point $overleftrightarrow{ae}$ intersects $overleftrightarrow{cd}$ at point _________.

Explanation:

Question 6

Step1: Define statements

Let $p$: Negotiations fail, $q$: Baseball strike does not end, $r$: World - Series is played, $s$: Baseball strike has ended. The given statements are $p
ightarrow q$ and $r
ightarrow s$. Also, $
eg q$ is the opposite of $q$ and $
eg s$ is the opposite of $s$.

Step2: Analyze implications

We know that $p
ightarrow q$ and $r
ightarrow s$. If $p$ is true (negotiations fail), then $q$ is true (strike does not end). But if $r$ is true (World - Series is played), then $s$ is true (strike has ended). If negotiations fail ($p$), since $p
ightarrow q$ (strike does not end), and $r
ightarrow s$ (if World - Series, strike ends), for consistency, if $p$ is true, $r$ must be false. That is, if negotiations fail, the World - Series will not be played.

By observing the given diagram of the intersecting lines $\overleftrightarrow{AE}$ and $\overleftrightarrow{CD}$, we can see the point of intersection.

Answer:

If negotiations fail, the World Series will not be played.

Question 7