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

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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
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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.
 
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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.
 

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I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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