Math / Discrete

QuestionIf possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements given below.
If you get an A on your math homework, then you will pass the test. If you get an A on your math homework, then you will pass the class.
Answer Attempt 1 out of 4 If you pass the test, then you will pass the class. If you practice, then you will get an If you get an $A$ on your math homework, then you will get a 100 . $\square$ You cannot use the Law of A on your test. Syllogism to create a new conditional statement.

Studdy Solution

STEP 1

1. The Law of Syllogism states that if we have two conditional statements, "If $p$ , then $q$ " and "If $q$ , then $r$ ", we can derive a new conditional statement "If $p$ , then $r$ ".
2. The given statements must be logically connected to apply the Law of Syllogism.

STEP 2

1. Identify the given conditional statements.
2. Verify that the statements are logically connected to apply the Law of Syllogism.
3. Formulate the new conditional statement using the Law of Syllogism.

STEP 3

Identify the first conditional statement: "If you get an A on your math homework, then you will pass the test." Let $p$ be "you get an A on your math homework" and $q$ be "you will pass the test".
$p \rightarrow q$

STEP 4

Identify the second conditional statement: "If you get an A on your math homework, then you will pass the class." Let $p$ be "you get an A on your math homework" and $r$ be "you will pass the class".
$p \rightarrow r$

STEP 5

Verify the logical connection: The statements share the same antecedent $p$ ("you get an A on your math homework"), but they do not share the consequent directly as required by the Law of Syllogism.

STEP 6

Since the statements do not follow the exact form required for the Law of Syllogism ( $q \rightarrow r$ ), we cannot directly apply the Law of Syllogism to form a new conditional statement in this case.

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Studdy Solution

STEP 1

1. The Law of Syllogism states that if we have two conditional statements, "If $p$ , then $q$ " and "If $q$ , then $r$ ", we can derive a new conditional statement "If $p$ , then $r$ ".
2. The given statements must be logically connected to apply the Law of Syllogism.

STEP 2

1. Identify the given conditional statements.
2. Verify that the statements are logically connected to apply the Law of Syllogism.
3. Formulate the new conditional statement using the Law of Syllogism.

STEP 3

Identify the first conditional statement: "If you get an A on your math homework, then you will pass the test." Let $p$ be "you get an A on your math homework" and $q$ be "you will pass the test".
$p \rightarrow q$

STEP 4

Identify the second conditional statement: "If you get an A on your math homework, then you will pass the class." Let $p$ be "you get an A on your math homework" and $r$ be "you will pass the class".
$p \rightarrow r$

STEP 5

Verify the logical connection: The statements share the same antecedent $p$ ("you get an A on your math homework"), but they do not share the consequent directly as required by the Law of Syllogism.

STEP 6

Since the statements do not follow the exact form required for the Law of Syllogism ( $q \rightarrow r$ ), we cannot directly apply the Law of Syllogism to form a new conditional statement in this case.

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Studdy Solution

STEP 1

1. The Law of Syllogism states that if we have two conditional statements, "If ppp, then qqq" and "If qqq, then rrr", we can derive a new conditional statement "If ppp, then rrr".2. The given statements must be logically connected to apply the Law of Syllogism.

STEP 2

1. Identify the given conditional statements.2. Verify that the statements are logically connected to apply the Law of Syllogism.3. Formulate the new conditional statement using the Law of Syllogism.

STEP 3

Identify the first conditional statement: "If you get an A on your math homework, then you will pass the test." Let ppp be "you get an A on your math homework" and qqq be "you will pass the test".p→q p \rightarrow q p→q

STEP 4

Identify the second conditional statement: "If you get an A on your math homework, then you will pass the class." Let ppp be "you get an A on your math homework" and rrr be "you will pass the class".p→r p \rightarrow r p→r

STEP 5

Verify the logical connection: The statements share the same antecedent ppp ("you get an A on your math homework"), but they do not share the consequent directly as required by the Law of Syllogism.

STEP 6

Since the statements do not follow the exact form required for the Law of Syllogism (q→rq \rightarrow rq→r), we cannot directly apply the Law of Syllogism to form a new conditional statement in this case.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The Law of Syllogism states that if we have two conditional statements, "If $p$ , then $q$ " and "If $q$ , then $r$ ", we can derive a new conditional statement "If $p$ , then $r$ ".
2. The given statements must be logically connected to apply the Law of Syllogism.

1. Identify the given conditional statements.
2. Verify that the statements are logically connected to apply the Law of Syllogism.
3. Formulate the new conditional statement using the Law of Syllogism.

Identify the first conditional statement: "If you get an A on your math homework, then you will pass the test." Let $p$ be "you get an A on your math homework" and $q$ be "you will pass the test".
$p \rightarrow q$

Identify the second conditional statement: "If you get an A on your math homework, then you will pass the class." Let $p$ be "you get an A on your math homework" and $r$ be "you will pass the class".
$p \rightarrow r$

Verify the logical connection: The statements share the same antecedent $p$ ("you get an A on your math homework"), but they do not share the consequent directly as required by the Law of Syllogism.

Since the statements do not follow the exact form required for the Law of Syllogism ( $q \rightarrow r$ ), we cannot directly apply the Law of Syllogism to form a new conditional statement in this case.