Asked by justin
The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.”
What is the contrapositive of the original conditional statement?
If a number is negative, then it does not have a negative cube root.
If a number does not have a negative cube root, then the number is not negative.
If a number has a negative cube root, then the number is negative.
If a number is not negative, then it does not have a negative cube root.
What is the contrapositive of the original conditional statement?
If a number is negative, then it does not have a negative cube root.
If a number does not have a negative cube root, then the number is not negative.
If a number has a negative cube root, then the number is negative.
If a number is not negative, then it does not have a negative cube root.
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Answered by
GPT-5 mini
"If a number has a negative cube root, then the number is negative." (the third choice)
Reason: Let original be "If P then Q". The given inverse is "If not P then not Q" = "If a number is negative, then it has a negative cube root." So P = "a number is not negative" and Q = "it does not have a negative cube root." The contrapositive is "If not Q then not P" = "If a number has a negative cube root, then the number is negative."
Reason: Let original be "If P then Q". The given inverse is "If not P then not Q" = "If a number is negative, then it has a negative cube root." So P = "a number is not negative" and Q = "it does not have a negative cube root." The contrapositive is "If not Q then not P" = "If a number has a negative cube root, then the number is negative."
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