Question

express the following statement in \if...then\ form. then write the statements converse, inverse, contrapositive, and negation. no headache is sufficient for no aspirin. write the statement in \if...then\ form. choose the correct answer below. a. if there is no aspirin, then there is no headache. b. if there is a headache, then there is an aspirin. c. if there is no headache, then there is no aspirin. d. if there is a headache, then there is no aspirin. e. if there is no headache, then there is an aspirin. f. if there is an aspirin, then there is a headache.

Explanation:

The statement "No headache is sufficient for no aspirin" means that the absence of a headache implies the absence of the need for aspirin. In "if...then" form, it is "If there is no headache, then there is no aspirin".
For the converse of a conditional statement "if p then q" is "if q then p".
The inverse is "if not p then not q".
The contra - positive is "if not q then not p" and the negation is the opposite of the original statement.

Answer:

1. "if...then" form: C. If there is no headache, then there is no aspirin.
2. Converse: A. If there is no aspirin, then there is no headache.
3. Inverse: B. If there is a headache, then there is an aspirin.
4. Contra - positive: F. If there is an aspirin, then there is a headache.
5. Negation: There is no headache and there is an aspirin.