Section 2-2: Biconditionals
and Definitions
2.01 Use logic and deductive
reasoning to draw conclusions and
solve problems.
Essential Questions
1) How are if-then statements written and
interpreted?
2) How are Venn diagrams used to draw
conclusions?
Homework Answers
• P 74: 64) A 65) I 66) D 67) If Marta is too
young to vote, then she is 5 years old. False
• P 269-270: 42) D 43) G 44) D 45) H
• Complete: Check Skills, p 75 (all)
Logically equivalent
The statement and its contrapositive are
logically equivalent.
This means that the statement and its
contrapositive are both true or both false.
Draw concentric circles for the Venn diagram for
testing conclusions for the conditional and the
contrapositive.
The hypothesis of each goes in the inner circle and the
conclusion goes in the outer ring. If the statement
one is asked to draw a conclusion about does not
coincide with a hypothesis, there is no conclusion.
biconditional
A statement that combines a conditional and
its converse with the words “if and only if”
(abbreviated iff).
Examples: Worksheet Conditional Conclusions
Together: 1 -9 odds
You: 2 – 8 evens
Worksheet: 4 Questions on Biconditionals
Together: 1, 3
You : 2, 4
linear pair
two adjacent angles that are supplementary
• With a partner, complete p 78 (2 – 22 even)
• Individually: Practice 2-2
• P 78: 2) If 2x-5=19, then x=12. True. X=12 iff 2x5=19. 4) If |x|=3, then x=3. False since |-3|= 3.
6) If x2 = 100, then x = -10. It is false since x can
also equal 10. 8) If an integer is divisible by 100,
then its last 2 digits are zeros. If an integer’s last
2 digits are zeros, then it is divisible by 100. 10) If
2 lines are II, then they are coplanar and do not
intersect. If 2 lines are coplanar and do not
intersect, then they are II. 12) If x2 = 144, then
x=12 or x = -12. If x = 12 or x = -12, then x2 = 144.
14) Planes are II if and only if they do not
intersect. 16) not reversible 18) No; it isn’t
reversible. Counter: mouse 20) No; not precise; a
ray or pt. could be part of a line. 22) No; not
reversible. Counter: stop sign
Summarize
Lesson Quiz 2-2
Homework
If-Then statements, Converses Worksheet
Mixed Review, p 81 (55 – 69)