Question

represent each true statement with symbols. use symbols to write related contrapositives of the conditionals. then use the law of detachment and the law of syllogism to draw a conclusion. if avery draws a numbered card from 4 to 10, then his game - piece moves to home base. if his game - piece moves to home base, he wins the game. avery does not win. represent the statements as follows. p: avery draws a numbered card from 4 to 10 q: avery moves his game - piece into home base r: avery wins the game. this means the first statement is represented with _, the second statement is represented with _, and the third statement is represented with _

Explanation:

Step1: Identify the conditional statements

The first statement "If Avery draws a numbered card from 4 to 10, then his game - piece moves to home base" can be written as $p
ightarrow q$. The second statement "If his game - piece moves to home base, he wins the game" can be written as $q
ightarrow r$. The third statement "Avery does not win" is $
eg r$.

Step2: Use the contrapositive

The contrapositive of $q
ightarrow r$ is $
eg r
ightarrow
eg q$. Since we know $
eg r$ (Avery does not win), by the Law of Detachment, we can conclude $
eg q$ (Avery's game - piece does not move to home base).

Step3: Use the contrapositive again

The contrapositive of $p
ightarrow q$ is $
eg q
ightarrow
eg p$. Since we have $
eg q$ (Avery's game - piece does not move to home base), by the Law of Detachment, we can conclude $
eg p$ (Avery did not draw a numbered card from 4 to 10).

Answer:

The first statement is represented with $p
ightarrow q$, the second statement is represented with $q
ightarrow r$, and the third statement is represented with $
eg r$. The conclusion is that Avery did not draw a numbered card from 4 to 10.