 If an integer ends with 0, then the integer is divisible by 2.  What is the truth value of the above conditional?  What is the converse?  What is.

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Presentation transcript:

 If an integer ends with 0, then the integer is divisible by 2.  What is the truth value of the above conditional?  What is the converse?  What is the truth value of the converse?

 Go over hmwk 2-1

10/3

 I can write a biconditional given a conditional and it’s converse.

 Biconditional: When the conditional and its converse are both true, you can combine them into one statement called a biconditional. You connect them with the phrase if and only if.

 Writing a biconditional  First, determine if the conditional and converse are true. They both must be true  Second, go to the conditional, and take out IF from the beginning.  Third, replace the word THEN with “if and only if”

 Example:  Conditional: If two angles have the same measure, then the angles are congruent  Converse:  Truth Values:  Biconditional:

 Example:  Conditional: If three points are collinear, then they lie on the same line.  Converse:  Truth Values:  Biconditional:

 Separating a biconditional  This is taking a biconditional and coming up with the conditional and it’s converse.

 Example  Biconditional: A number is divisible by 3 if and only if the sum of its digits is divisible by 3  Conditional:  Converse:

 Example  Biconditional: A number is prime if and only if it has two distinct factors, 1 and itself  Conditional:  Converse:

 Use clearly understood or already defined terms.  Are precise. Avoid general words such as some, sort of, big, small.  Are reversible. You can write a good definition as a biconditional.

 Definition: Perpendicular lines are two lines that intersect to form right angles  Conditional: if two lines are perpendicular, then they intersect to form right angles  Converse: if two lines intersect to form right angles, then they are perpendicular  Biconditional: Two lines are perpendicular if and only if they intersect to form right angles

 Definition: A right angle is an angle whose measure is 90  Conditional:  Converse:  Biconditional:

 2-2 in the Packet  #1-12

 Homework  P # 2-22 even; 32-35