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 p→q, the second statement is represented with q→r, and the third statement is represented with ¬r. by the law of blank the first two statements can be combined to make the true conditional blank

Explanation:

Step1: Identify given statements

Let \(p\): Avery draws a numbered card from 4 - 10, \(q\): Avery moves his game - piece to home base, \(r\): Avery wins the game. The statements are \(p
ightarrow q\), \(q
ightarrow r\), and \(
eg r\).

Step2: Use the Law of Syllogism

The Law of Syllogism states that if \(a
ightarrow b\) and \(b
ightarrow c\), then \(a
ightarrow c\). Here, since \(p
ightarrow q\) and \(q
ightarrow r\), by the Law of Syllogism, we get \(p
ightarrow r\).

Step3: Use the Law of Detachment

The Law of Detachment states that if \(a
ightarrow b\) and \(
eg b\), then \(
eg a\). We have \(p
ightarrow r\) and \(
eg r\). So, by the Law of Detachment, \(
eg p\).

Answer:

Avery did not draw a numbered card from 4 to 10.