Question

Rephrase in contrapositive form:

(a) "If you are taller than 6 ft, then it is unpleasant for you to travel in economy class." Your contrapositive must not contain explicit references to negation. Assume that the negation of "unpleasant" is "pleasant".

(b) "If x ≥ 0 and y ≥ 0 then xy ≥ 0" where x, y are real numbers.

Answer 1

Explanation:

Consider the provided information.

For the condition statement
`p \rightarrow q` or equivalent "If p then q"

The rule for Contrapositive is: Negative both statements and interchange them.
`\sim q \rightarrow \sim p`

Part (A) If you are taller than 6 ft, then it is unpleasant for you to travel in economy class.

Here p is "you are taller than 6 ft, and q is "it is unpleasant for you to travel in economy class".

It is given that Your contrapositive must not contain explicit references to negation. Assume that the negation of "unpleasant" is "pleasant".

Contrapositive: If it is pleasant for you to travel in economy class then you are not taller than 6 ft then.

Part (B) "If x ≥ 0 and y ≥ 0 then xy ≥ 0" where x, y are real numbers.

Here p is "xy≥ 0, and q is "x ≥ 0 and y ≥ 0"

The negative of xy≥ 0 is xy<0, x ≥ 0 is x<0 and y ≥ 0 is y<0.

Remember negative means opposite.

Contrapositive: If xy < 0 then x<0 and y<0.