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]
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.
Solution
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:
Conditional (If p, then q)
Converse (If q, then p)
Inverse (If not p, then not q)
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:
Conditional: \( \text{If } p, \text{ then } q \)
Converse: \( \text{If } q, \text{ then } p \)
Inverse: \( \text{If not } p, \text{ then not } q \)
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:
"If it is an elephant, then it has purple spots." matches the Conditional form: \( \text{If } p, \text{ then } q \).
"If it has purple spots, then it is an elephant." matches the Converse form: \( \text{If } q, \text{ then } p \).
"If it is not an elephant, then it does not have purple spots." matches the Inverse form: \( \text{If not } p, \text{ then not } q \).
"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
\(\boxed{\text{If it is an elephant, then it has purple spots.}} \)