Chapter B.2, Problem 15E

Solution

(a.)

To Write: The given statement in if-then form.

It has been determined that the given statement can be written in if-then form as follows:

If a figure is a square, then it is a rectangle.

Given:

Every figure that is a square is a rectangle.

Concept used:

Statements with universal quantifiers and most other conjunctions can be written in if-then form.

Calculation:

The given statement is:

Every figure that is a square is a rectangle.

Writing in if-then form as follows:

If a figure is a square, then it is a rectangle.

Conclusion:

It has been determined that the given statement can be written in if-then form as follows:

If a figure is a square, then it is a rectangle.

(b.)

To Write: The given statement in if-then form.

It has been determined that the given statement can be written in if-then form as follows:

If a number is an integer, then it is a rational number.

Given:

All integers are rational numbers.

Concept used:

Statements with universal quantifiers and most other conjunctions can be written in if-then form.

Calculation:

The given statement is:

All integers are rational numbers.

Writing in if-then form as follows:

If a number is an integer, then it is a rational number.

Conclusion:

It has been determined that the given statement can be written in if-then form as follows:

If a number is an integer, then it is a rational number.

(c.)

To Write: The given statement in if-then form.

It has been determined that the given statement can be written in if-then form as follows:

If a figure is a triangle, then it has exactly three sides.

Given:

Figures with exactly three sides maybe triangles.

Concept used:

Statements with universal quantifiers and most other conjunctions can be written in if-then form.

Calculation:

The given statement is:

Figures with exactly three sides maybe triangles.

Writing in if-then form as follows:

If a figure is a triangle, then it has exactly three sides.

Conclusion:

It has been determined that the given statement can be written in if-then form as follows:

If a figure is a triangle, then it has exactly three sides.

(d.)

To Write: The given statement in if-then form.

It has been determined that the given statement can be written in if-then form as follows:

If it rains, then it is cloudy.

Given:

It rains only if it is cloudy.

Concept used:

Statements with universal quantifiers and most other conjunctions can be written in if-then form.

Calculation:

The given statement is:

It rains only if it is cloudy.

Writing in if-then form as follows:

If it rains, then it is cloudy.

Conclusion:

It has been determined that the given statement can be written in if-then form as follows:

If it rains, then it is cloudy.