Set Theory
What are the objects inside a set called?
Elements
One set inside another set is called a subset.
True
P: It is 3:24 pm. Q: It is time to go home.
Make a conditional statement.
If it is 3:24 pm, then it is time to go home.
All corresponding sides of both triangles are equal.
Experimental Probability
What actually happens
A: {2, 3, 4, 5, 8} B: {1, 6, 7}
What is the intersection of these two sets?
Empty set { }
A compound statements are formed by combining two or more simple statements.
True
P: It is 3:24 pm Q: It is time to go home.
~P -> Q
If it is not 3:24 pm, then it is time to go home.
The corresponding sides length of two triangles have a ratio of 2:1.
Similar
Theoretical Probability
What Should Happen
A: {2, 4, 6, 8, 10} B: {4, 6, 10}
What is the Union of these two sets?
{2, 4, 6, 8, 10}
It is after 5 pm.
This is an example of a compound statement.
False
It is a simple statement.
P: It is 3:24 pm Q: It is time to go home.
~P -> ~Q
If it is not 3:24 pm, then it is not time to go home.
All the corresponding angles of two triangles are congruent.
Both similar and congruent by the ~AA Theorem.
Bi-conditional Statement
A statement that is true only when the component statements have the same truth value.
What is the probability of heads when flipping a coin?
50% or 1/2
The P and Q of a conditional statement can be called the "Antecedent" and "Consequent".
True:
The hypothesis is the Antecedent and the Conclusion is the Consequent.
P: A student studies. Q: A student does their homework. R: The student passes the class. P ^ Q -> R
If a student studies and a student does their homework, then the student passes the class.
When two figures have two corresponding side lengths that are at a ratio of 2:1 and the third corresponding side has the ratio of 1.5:1.
Neither
Implications
Conditional statements that are tautologies
What is the probability of rolling a seven from a dice?
{ } The same has finding four legs on a chicken.
If one angle and the adjacent sides are congruent to the corresponding angle and sides of another triangle, then the triangles are congruent. If there a postulate to confirm this?
True, SAS Theorem.
P: A student misses lecture. Q: A student studies. R: A student fails. (Q ^ ~P) -> ~R
A student studies and a students does not miss a lecture, then the student does not fail.
A rectangle that one pair of sides is longer than the other pair; and a square.
Neither
Tautology
A compound statements that is always true.