2.1 Conditional Statements. Conditional Statement – a logical statement with two parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If p, then q is symbolized as p -> q (p implies q). Ex: If you study hard, then you will get As.
P, the “if part”, hypothesis
Q, the “then part”, conclusion
If p, then q is symbolized as p -> q (p implies q).
If you study hard, then you will get As.
If you live in Ridgewood, then you live in NJ.
If an angle is 28 degrees, then it is acute.
Now go back and underline the hypothesis and circle the conclusions.
The negation of a statement is the
opposite of the original statement.
Symbol: ~p Words: not p
Examples: Find the negation of the statement.
Given Conditional Statement: p->q
Converse: Switch hypothesis and conclusion.
Inverse: Negate hypothesis and conclusion.
Contrapositive: Switch and negate the hypothesis and conclusion.
A counterexample is a case that fits the hypothesis but leads to a different conclusion.
You can prove a statement is false by finding a counterexample.
Practice finding counterexamples.
1) If a number is prime, then it is odd.
2) If you live in Ridgewood, you go to RHS.
3) If a food is round, then it is pizza.
4) If a 3D figure lacks vertices, it is a sphere.
Converse: If you are a musician, then you are a guitar player. T or F
Inverse: If you are not a guitar player, then you are not a musician. T or F
Contrapositive. If you are not a musician, then you are not a guitar player. T or F
Associate CONverse with SWITCHING the hypothesis and conclusion
No Strings Attached
Everyone will have to share, so make sure you come up with something.
When a conditional statement and its converse are true, you can write them as a single biconditional statement linking the hypothesis and conclusion with “if and only if”.
Words: p if and only if q Symbol: p <-> q
Write a biconditional statement for your conditional statement if both your conditional and converse were true. If not, write one for perpendicular lines.