No of Indian men=23
No of Indian women=29
Fixed No. of Dentists in whole=4
Fixed No. of (men+dentists)= 24

women which are dentist + men which are dentist + men which are not dentist= 24
x + (4-x) + {23-(4-x)} = 24
we get, x = 1 (Ans)

To solve this problem, we need to use the principles of set theory and basic algebra. Let's break down the information given:

- There were 23 Indian men and 29 Indian women at the meeting.
- There were 4 dentists in total, and all of them were Indian.
- There were 24 individuals who were either men or dentists.

We need to find the number of women dentists at the meeting.

Let's define some variables to represent the different groups:

- Let M represent the set of men.
- Let W represent the set of women.
- Let D represent the set of dentists.

Now, let's translate the given information into equations:

- The total number of people at the meeting is 100, so we have:
|M ∪ W| = 100

- There were 23 Indian men and 29 Indian women, so we have:
|M ∩ D| = 23
|W ∩ D| = ?

- There were 4 dentists in total, and all of them were Indian, so we have:
|D| = 4

- There were 24 individuals who were either men or dentists, so we have:
|M ∪ D| = 24

Now, let's use these equations to find the number of women dentists.

First, we can use the principle of inclusion-exclusion to find the total number of dentists:
|D| = |M ∩ D| + |W ∩ D| - |M ∩ W ∩ D|

Since we know that |D| = 4 and |M ∩ D| = 23, we can substitute these values into the equation to solve for |W ∩ D|:

4 = 23 + |W ∩ D| - |M ∩ W ∩ D|

Next, we can use the equation |M ∪ D| = 24 to find |M ∩ W ∩ D|:

|M ∪ D| = |M| + |D| - |M ∩ D|

Since we know that |M ∪ D| = 24, |M| = 23, and |M ∩ D| = 23, we can substitute these values into the equation to solve for |M ∩ W ∩ D|:

24 = 23 + 4 - |M ∩ W ∩ D|

Simplifying the equation:

1 = -|M ∩ W ∩ D|

Since the number of individuals in a set cannot be negative, we can conclude that |M ∩ W ∩ D| = 0.

Now, let's substitute this value back into the equation for |W ∩ D|:

4 = 23 + |W ∩ D| - 0

Simplifying the equation:

|W ∩ D| = 4 - 23 = -19

Again, the number of individuals in a set cannot be negative, so we can conclude that |W ∩ D| = 0.

Therefore, there were no women dentists at the meeting. The correct answer is option A) 1.