Question

1. conditional: if a polygon has 3 sides, then it is a triangle. which is the contrapositive? a. if a polygon is not a triangle, then it does not have 3 sides. b. if a polygon does not have 3 sides, then it is not a triangle. c. if a polygon has 3 sides, then it is a triangle. d. if a polygon is a triangle, then it has 3 sides. 6. which of the following conditionals is false? a. if a number is even, then it is divisible by 2. b. if an angle is 90°, then it is a right angle. c. if a shape is a rectangle, then it has 4 sides. d. if a quadrilateral is a square, then it is a triangle. 7. if you are given the statement if p, then q. which of the following represents its contrapositive? a. if q, then p. b. if not p, then not q. c. if not q, then not p. d. if q, then not p. 8. the statement is: if a student studies, then they will pass the test. the related statement is: if a student does not study, then they will not pass the test. this is the: a. converse b. inverse c. contrapositive d. biconditional 9. which of the following is a biconditional? a. if today is monday, then tomorrow is tuesday. b. a shape is a triangle if and only if it has 3 sides. c. if a polygon has 3 sides, then it is a triangle. d. if a shape is a triangle, then it has 3 sides.

Explanation:

5.

The contrapositive of a statement “If \(p\), then \(q\)” is “If not \(q\), then not \(p\)”. Here \(p\) is “a polygon has 3 sides” and \(q\) is “it is a triangle”. So the contrapositive is “If a polygon is not a triangle, then it does not have 3 sides”.

A quadrilateral has 4 sides. A triangle has 3 sides. A square is a quadrilateral. So the statement “If a quadrilateral is a square, then it is a triangle” is false because a square cannot be a triangle.

The contrapositive of the statement “If \(p\), then \(q\)” is “If not \(q\), then not \(p\)”.

Answer:

A. If a polygon is not a triangle, then it does not have 3 sides.

6.