Biconditionals and Logical Equivalence

Which Conditional Statement has a false Biconditional?

• If two angles are vertical, then they are congruent.

• If two angles have the same measure, then they are congruent.

• If a polygon has only four sides, then the polygon is a quadrilateral.

• If two lines do not intersect, then they are parallel.

Which conditional statement has a false biconditional?

• If all 3 sides of a triangle are congruent, then it is an equilateral triangle.

• If all sides of a polygon are congruent,

  then it is a regular polygon.

• If all sides of quadrilateral are congruent, then it is a square.

• If a quadrilateral has only one pair of opposite congruent sides, then it is an isosceles trapezoid.

Which related conditional will always have the same truth value as the Inverse.

• Biconditional

• Original Conditional

• Contrapositive

• Converse

Which two statements will always be logically equivalent?

• Original Conditional and Inverse

• Converse and Contrapositive

• Original Conditional and Contrapositive

• Inverse and Contrapositive

What is logically equivalent to p → q?

• q → p
• ~ p → ~ q
• p → ~ q
• ~ q → ~ p

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

• if

• then

• if and only if

• always

Select the conditional statement of the biconditional statement.

Points are collinear if and only if they all lie in one line.

• If collinear points lie in one line, then they are a line.

• If points all lie in one line, then they are collinear.

• Collinear points lie in one line.

• If points are collinear, then they all lie in one line.

Write the conditional statements as a biconditional statement:

1) If B is between A and C, then AB+BC=AC.

• Segment Addition Postulate

• B is between A and C when AB+BC=AC if and only if Segment Addition Postulate.

• B is between A and C if and only if AB+BC=AC.

When can a biconditional statement be true?

• When the inverse and the converse are both true
• When the original statement (conditional statement) & the contrapositive are both true.
• When the converse is true.
• When the original statement (conditional statement) and the converse are both true.

Select the conditional statement of the biconditional statement:

I am a junior if and only if I am in 11th grade.

• I am a junior

• If I am a junior, then I am in 11th grade.

• I am in 11th grade