Question

Given the statement, If a and b are negative then a times b is negative. This statement: If a times b is not negative then a and b are not negative is which of the following?

a.converse

b. negation

c. contrapositive

Answer 1

Answer: (c.) contrapositive

Explanation:

Statement 1 ⇒ If a <0 and b<0 then, (a
`*`b)<0

Statement 2 ⇒ If (a
`*`b)>0, then a >0 and b>0

Lets assume that,

a is not negative be A

b is not negative be B

(a
`*`b) is not negative be C

then,

Statement 1 ⇒ (¬A ∧ ¬B) ⇒(¬C)

Statement 2 ⇒ C ⇒ (A ∧ B)

Hence, the statement is contrapositive.