Conditional and Biconditional statement and Reasoning

A statement that can be expressed as if-then statements.

• Conditional statements

• Biconditional statements

• Converse

• Inverse

What type of statement is formed when both a conditional statement and its converse are true, often expressed using “if and only if”?

• Conditional statements

• Biconditional statements

• Converse

• Inverse

Which of the following is a conditional statement?

• The sky is blue.

• If it rains, then the ground gets wet.

• The ground is wet if it rains.

• Rain makes the ground wet.

Which of the following represents a biconditional statement?

• If a polygon is a triangle, then it has three sides.

• A polygon is a triangle if and only if it has three sides.

• A polygon is a triangle if it has three sides.

• If a polygon has three sides, then it is a triangle.

A biconditional statement is true when:

• Both the conditional and converse are true.

• Both the conditional and inverse are true.

• Only the conditional is true.

• Only the converse is true.

What type of property of equality is this, where for every real number x, x = x?

What type of property of equality is this, where for any real number x or y,

if x = y, then y = x?

What type of property of equality is this, where for any real number x, y, or z,

if x = y and y = z, then x = z?

What type of property of equality is this, where for any real number x, y, or z,

if x = y, then x + z = y + z?

What type of property of equality is this, where for all real number x, y, or z,

x(y + z) = xy +xz?