Let A= sets of all letter in the word MATHEMATICS
and B= sets of all letters in the word STATISTICS.
Find `A cap B`.

Answer

To solve the problem, we need to find the intersection of the sets A and B, which are defined by the letters in the words "MATHEMATICS" and "STATISTICS".

### Step-by-Step Solution:

1. **Identify the letters in the word "MATHEMATICS"**:
- The letters are: M, A, T, H, E, M, A, T, I, C, S.
- Now, we will create set A by taking only unique letters:
- Set A = {M, A, T, H, E, I, C, S}.

2. **Identify the letters in the word "STATISTICS"**:
- The letters are: S, T, A, T, I, S, T, I, C, S.
- Now, we will create set B by taking only unique letters:
- Set B = {S, T, A, I, C}.

3. **Find the intersection of sets A and B (A ∩ B)**:
- The intersection consists of elements that are present in both sets A and B.
- From set A = {M, A, T, H, E, I, C, S} and set B = {S, T, A, I, C}, we can identify the common elements:
- S is in both A and B.
- T is in both A and B.
- A is in both A and B.
- I is in both A and B.
- C is in both A and B.

4. **Write the intersection set**:
- Therefore, A ∩ B = {S, T, A, I, C}.

### Final Answer:
A ∩ B = {S, T, A, I, C}.

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