Questions: Given the phrases: p: it is an elephant q : it has purple spots Match the correct term to each if-then statement. If it is an elephant, then it has purple spots. [Choose] If it has purple spots, then it is an elephant. [Choose] If it is not an elephant, then it does not have [Choose] purple spots. If it doesn't have purple spots, then it is not an elephant. [Choose]

Given the phrases:
p: it is an elephant
q : it has purple spots

Match the correct term to each if-then statement.

If it is an elephant, then it has purple spots. 
[Choose]

If it has purple spots, then it is an elephant.
[Choose]

If it is not an elephant, then it does not have
[Choose] purple spots. 

If it doesn't have purple spots, then it is not an elephant.
[Choose]
Transcript text: Given the phrases: p: it is an elephant q : it has purple spots Match the correct term to each if-then statement. If it is an elephant, then it has purple spots. $\square$ [Choose] If it has purple spots, then it is an elephant. [Choose] If it is not an elephant, then it does not have [Choose] purple spots. $\square$ If it doesn't have purple spots, then it is not an [Choose] elephant.
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Solution

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Solution Steps

To match the correct term to each if-then statement, we need to identify the logical structure of each statement and match it with the appropriate logical form. The logical forms we are dealing with are:

  1. Conditional (If p, then q)
  2. Converse (If q, then p)
  3. Inverse (If not p, then not q)
  4. Contrapositive (If not q, then not p)
Step 1: Identify the Logical Forms

We need to identify the logical forms of the given statements. The logical forms are:

  1. Conditional: \( \text{If } p, \text{ then } q \)
  2. Converse: \( \text{If } q, \text{ then } p \)
  3. Inverse: \( \text{If not } p, \text{ then not } q \)
  4. Contrapositive: \( \text{If not } q, \text{ then not } p \)
Step 2: Match the Statements to Logical Forms

Given the phrases:

  • \( p \): it is an elephant
  • \( q \): it has purple spots

We match each statement to its corresponding logical form:

  1. "If it is an elephant, then it has purple spots." matches the Conditional form: \( \text{If } p, \text{ then } q \).
  2. "If it has purple spots, then it is an elephant." matches the Converse form: \( \text{If } q, \text{ then } p \).
  3. "If it is not an elephant, then it does not have purple spots." matches the Inverse form: \( \text{If not } p, \text{ then not } q \).
  4. "If it doesn't have purple spots, then it is not an elephant." matches the Contrapositive form: \( \text{If not } q, \text{ then not } p \).

Final Answer

\(\boxed{\text{If it is an elephant, then it has purple spots.}} \)

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