select the correct statement (s)

Options

A. (a) A cubic system possesses a total of 23 elements of symmetry
B. (b) A cubic contains centre of symmetry , planes of symmetry as well as axes of symmetry
C. (c) For triclinic system `ane b ne c and alpha ne beta ne gammane 90^(@)`
D. (d) The total no. of Bravais space lattic belonging ta all the seven crystals are 14

Answer

To solve the question regarding the correct statements about the solid state, we need to analyze each statement provided.

### Step-by-Step Solution:

1. **Statement A**: "A cubic system possesses a total of 23 elements of symmetry."
- **Analysis**: This statement is true. In a cubic crystal system, there are indeed 23 elements of symmetry, which include rotations, reflections, and inversions.

2. **Statement B**: "A cubic contains center of symmetry, planes of symmetry, as well as axes of symmetry."
- **Analysis**: This statement is also true. A cubic crystal has:
- 1 center of symmetry
- 9 planes of symmetry (3 planes through the center and 6 diagonal planes)
- 13 axes of symmetry (4 three-fold axes, 6 two-fold axes, and 3 four-fold axes).

3. **Statement C**: "For a triclinic system, A ≠ B ≠ C; α ≠ β ≠ γ."
- **Analysis**: This statement is true. In a triclinic crystal system, the lengths of the axes (A, B, and C) are all different, and the angles (α, β, and γ) between them are also different.

4. **Statement D**: "The total number of Bravais lattices belonging to all the seven crystal systems is 14."
- **Analysis**: This statement is true. There are indeed 14 distinct Bravais lattices that can be classified under the seven crystal systems.

### Conclusion:
All four statements (A, B, C, and D) are correct.

### Final Answer:
- **Correct Statements**: A, B, C, and D are all correct.

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