# Choice, Chance and Sensible Logic

• WMDhamnekar
In summary, the conversation discusses the division of an infinite plane by non-concurrent and non-parallel lines. It is mentioned that three lines divide the plane into 7 parts and four lines divide it into 10 parts. The conversation then poses a question about the division of space by multiple planes.
WMDhamnekar
MHB
Homework Statement
a) In how many parts, we can divide an infinite plane by n straight lines of which no two lines are parallel and no three lines are concurrent?
Relevant Equations
No relevant equations. We have to use sensible logic.
Three non-concurrent and non-parallel lines divide an infinite plane in 7 parts. and four non-concurrent and non-parallel lines divide an infinite plane into 10 parts.

Is this statement correct? If correct, we can proceed further to answer this question.

If incorrect, suggest me the appropriate rectification.

WMDhamnekar said:
four non-concurrent and non-parallel lines divide an infinite plane into 10 parts
Or is it 11 ?

##\ ##

WMDhamnekar
So, the answer to this question is ## 1+ \frac12 \cdot n \cdot (n+1)=\frac12\cdot(n^2 + n +2)##
Now , second part of this question:
In how many parts, can we divide an infinite space by n planes of which no four planes meet in a point and no two planes are parallel?

How would you answer this question?
I am working on this question.

WMDhamnekar said:
How would you answer this question?
Same strategy: 1 plane: 2 parts, 2 planes: 4, but then three planes: 8 parts !

WMDhamnekar

## 1. What is the difference between choice and chance?

Choice refers to the act of making a decision or selecting an option based on personal preference or reasoning. Chance, on the other hand, refers to the occurrence of events that are unpredictable and beyond our control.

## 2. How does sensible logic play a role in decision making?

Sensible logic involves using rational thinking and sound judgement to make decisions. It takes into account factors such as past experiences, available information, and potential outcomes to make the most logical and sensible choice.

## 3. Can chance be influenced by our choices?

While chance events are unpredictable, our choices can sometimes impact the likelihood of certain outcomes. For example, choosing to wear a seatbelt while driving may decrease the chances of getting injured in a car accident.

## 4. How does understanding choice, chance, and sensible logic benefit us?

Understanding these concepts can help us make more informed decisions and navigate through uncertain situations. It can also help us accept and cope with events that are out of our control.

## 5. Are there any limitations to using sensible logic in decision making?

While sensible logic can help us make logical decisions, it is not foolproof and can be influenced by biases, emotions, and other external factors. It is important to also consider other perspectives and gather all relevant information before making a decision.

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