# 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....

# 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

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### 2 Answers

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.

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**.

Answer:

**e) I and III** is correct choice.