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

In summary, Wolfram|Alpha is a useful tool for those interested in mathematics, as it can help with tasks like creating Venn diagrams to demonstrate the equivalence or non-equivalence of logical statements.
  • #1
barbara
10
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
  • #2
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: 48

What is a Venn diagram?

A Venn diagram is a visual representation of the relationships between different sets or categories. It uses overlapping circles or other shapes to show the common and unique elements among the sets.

What does "p v (q ^ r) = (p v q) ^ (p v r)" mean in a Venn diagram?

This equation represents the distributive property in a Venn diagram. It shows that the union of set p with the intersection of sets q and r is equal to the intersection of the union of sets p and q, and the union of sets p and r.

How can I use a Venn diagram to solve this equation?

You can use a Venn diagram by drawing three intersecting circles to represent sets p, q, and r. Then, fill in the common and unique elements within the circles to visually represent the equation. The overlapping areas will show the intersections and unions of the sets.

What is the importance of using a Venn diagram to understand equations?

Venn diagrams provide a visual representation of complex equations, making it easier to understand the relationships between different sets. They also help to identify patterns and similarities, making it easier to solve equations and make logical deductions.

Can Venn diagrams be used for more than three sets?

Yes, Venn diagrams can be used for any number of sets. However, as the number of sets increases, it becomes more challenging to accurately represent the relationships between them. In these cases, other visualization methods may be more appropriate.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
5K
  • Set Theory, Logic, Probability, Statistics
Replies
8
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
874
  • Set Theory, Logic, Probability, Statistics
Replies
9
Views
872
  • Calculus and Beyond Homework Help
Replies
24
Views
801
  • Set Theory, Logic, Probability, Statistics
Replies
16
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
874
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Back
Top