MHB Venn Diagram: p v (q ^ r) = (p v q) ^ (p v r)

  • Thread starter Thread starter barbara
  • Start date Start date
  • Tags Tags
    Diagram Venn
Click For Summary
The discussion focuses on demonstrating the equivalence of the logical expressions p v (q ^ r) and (p v q) ^ (p v r) using a Venn diagram. Participants are encouraged to visualize the union and intersection of sets to understand the relationships between the variables. Additionally, it is highlighted that the expression p v (q ^ r) is not equivalent to (p v q) ^ r, prompting users to explore this distinction independently. The use of resources like Wolfram|Alpha is recommended for further exploration and clarification of these concepts. Understanding these logical relationships is essential for grasping foundational principles in set theory and logic.
barbara
Messages
10
Reaction score
0
can someone give me show me a venn diagram that will satisfy this statement
Venn diagram to show that the statement p v (q ^ r) is equivalent to (p v q) ^ (p v r) and show that this statement is not equivalent to (p v q) ^ r.
 
Physics news on Phys.org
Here is the first half of your request:

Try to do the second one on your own-remember that the "vee" symbol represents UNION, and the "wedge" symbol represents INTERSECTION (when doing a Venn diagram):

View attachment 5083

Wolfram|Alpha (Wolfram|Alpha: Computational Knowledge Engine) is a great resource for budding mathematicians/students, and even just the interested lay-person.
 

Attachments

  • WolframAlpha--P_union_Q_intersect_R--2015-12-19_2248.jpg
    WolframAlpha--P_union_Q_intersect_R--2015-12-19_2248.jpg
    4.6 KB · Views: 111
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
7K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K