# In the following list, where is the second statement the negation of the first?

I. The Canucks won last year.
The Canucks lost last year.

II. A rhombus is a trapezoid.
A trapezoid is not a rhombus.

III. A square is a rectangle.
A square is not a rectangle.

a) I only b) II only c) III only d) I and II e) I and III

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The correct option is (E), both I and III.

The statement "The Canucks lost last year." is a negation of "The Canucks won last year." The first says that they won and the second says they lost.

Similarly, the statement, "A square is not a rectangle." is a negation of "A square is a rectangle." One says that a square is a rectangle and the other says that a square is not a rectangle.

The statements, "A rhombus is a trapezoid." and "A trapezoid is not a rhombus." are not negations of each other.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The   negation  of a proposition p is notp.

So if the propsition p is true , then  the propoitio notp is not true.

If the proposition p is not true ,then notp is true.

The truth table of P and not is as folows:

p       notp

T        F

F       T.

Therefore applying this to the pairs of staments given we easily determinne:

I. The Canucks won last year.
The Canucks lost last year.

The second stement is negation of the first , as it negates the truth (or false ) of the first.

II. A rhombus is a trapezoid.
A trapezoid is not a rhombus.

The first statement value is F. The  second statement is true. But it  is not the negation of the first , but the negation of  the proposition a trapezoid is a rhombus.

III. A square is a rectangle.
A square is not a rectangle.

P is true , p is not true form. So this a negation.