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What is the inverse of the following statement?

"If a shape has four sicies, then it is not a triangle."
If a shape has four sides, then it is a triangle.
If a shape is not a triangle, then it has four sides.
If a shape does not have four sides, then it is a triangle.
If a shape is a triangle, then it does not have four sides.

1 Answer

4 votes

Answer:

if a shape is a triangle, then it does not have four sides.

Explanation:

The inverse of the statement "If a shape has four sides, then it is not a triangle" is "If a shape is not a triangle, then it does not have four sides." To understand the inverse, we need to switch the original statement's "if" and "then" parts and negate both parts. The original statement has the form "If P, then Q." The inverse is "If not P, then not Q." In this case, P represents "a shape has four sides," and Q represents "it is not a triangle." To form the inverse, we negate both P and Q. Negating P gives us "a shape is not a triangle." Negating Q gives us "it does not have four sides." So, the inverse statement is "If a shape is not a triangle, then it does not have four sides."

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