If A={1,2,3}, B={4,5,6},C={1,2,3,9,6} then which of the following is not ture?

Options

A. `A cancelsubsetB`
B. `A subset C`
C. `A subset B`
D. `B cancelsubset C`

Answer

To determine which statement is not true regarding the sets A, B, and C, we will analyze the subsets and their relationships step by step.

Given:
- A = {1, 2, 3}
- B = {4, 5, 6}
- C = {1, 2, 3, 9, 6}

### Step 1: Check if A is a subset of B
A subset means that every element of set A must also be an element of set B.

- Elements of A: 1, 2, 3
- Elements of B: 4, 5, 6

Since none of the elements of A (1, 2, 3) are present in B (4, 5, 6), we conclude:
**A is not a subset of B.**

### Step 2: Check if A is a subset of C
Now, we will check if A is a subset of C.

- Elements of A: 1, 2, 3
- Elements of C: 1, 2, 3, 9, 6

All elements of A (1, 2, 3) are present in C (1, 2, 3, 9, 6), so we conclude:
**A is a subset of C.**

### Step 3: Check if B is a subset of A
Next, we will check if B is a subset of A.

- Elements of B: 4, 5, 6
- Elements of A: 1, 2, 3

Since none of the elements of B (4, 5, 6) are present in A (1, 2, 3), we conclude:
**B is not a subset of A.**

### Step 4: Check if B is a subset of C
Lastly, we check if B is a subset of C.

- Elements of B: 4, 5, 6
- Elements of C: 1, 2, 3, 9, 6

None of the elements of B (4, 5, 6) are present in C (1, 2, 3, 9, 6), so we conclude:
**B is not a subset of C.**

### Conclusion
From the analysis:
1. A is not a subset of B (True)
2. A is a subset of C (True)
3. A is a subset of B (Not True)
4. B is not a subset of A (True)
5. B is not a subset of C (True)

Thus, the statement that is **not true** is:
**A is a subset of B.**