Original Statement "If it's a garage sale, then it's a Sunday."
Statement 1 "If it's a Sunday, then it's a garage sale."
Statement 2 "If it's not a Sunday, then it's not a garage sale."
Statement 3 "If it's not a garage sale, then it's not a Sunday."
Which option is correct?
Statement 2 is a converse, and statement 3 is an inverse of the original statement.
Statement 1 is a converse, and statement 3 is a contrapositive of the original statement.
Statement 2 is an inverse, and statement 1 is a contrapositive of the original statement.
Statement 1 is a converse, and statement 3 is an inverse of the original statement.
The correct option is:
Statement 1 is a converse, and statement 3 is a contrapositive of the original statement.
To determine which option is correct, we need to understand the concepts of converse, inverse, and contrapositive.
Converse: This is formed by switching the hypothesis and the conclusion of the original statement. If the original statement is "If A, then B," then the converse would be "If B, then A."
Inverse: This is formed by negating both the hypothesis and the conclusion of the original statement. If the original statement is "If A, then B," then the inverse would be "If not A, then not B."
Contrapositive: This is formed by both switching the hypothesis and the conclusion, as well as negating them. If the original statement is "If A, then B," then the contrapositive would be "If not B, then not A."
Now, let's analyze the given statements:
Statement 1: "If it's a Sunday, then it's a garage sale."
This is the converse of the original statement, as it switches the hypothesis "garage sale" and the conclusion "Sunday."
Statement 2: "If it's not a Sunday, then it's not a garage sale."
This is the inverse of the original statement, as it negates both the hypothesis and the conclusion.
Statement 3: "If it's not a garage sale, then it's not a Sunday."
This is the contrapositive of the original statement, as it switches and negates both the hypothesis and the conclusion.
Based on this analysis, the correct option is:
Statement 1 is a converse, and statement 3 is a contrapositive of the original statement.