If P is the set of all parallelogram, and T is the set of all trapeziums, then `PnnT` is

Options

A. P
B. T
C. `phi`
D. none of these

Answer

To solve the problem, we need to determine the intersection of the set of all parallelograms (P) and the set of all trapeziums (T).

### Step-by-Step Solution:

1. **Define the Sets**:
- Let \( P \) be the set of all parallelograms.
- Let \( T \) be the set of all trapeziums.

2. **Understand the Properties of the Shapes**:
- A **parallelogram** is a quadrilateral with both pairs of opposite sides parallel.
- A **trapezium** (or trapezoid) is defined as a quadrilateral with at least one pair of parallel sides.

3. **Identify the Relationship**:
- Since all parallelograms have two pairs of sides that are parallel, they also meet the condition of having at least one pair of parallel sides, which means that every parallelogram is also a trapezium.

4. **Determine the Intersection**:
- The intersection of two sets \( P \) and \( T \) (denoted as \( P \cap T \)) includes all elements that are common to both sets.
- Since every parallelogram is a trapezium, the intersection \( P \cap T \) will contain all parallelograms.

5. **Conclusion**:
- Therefore, \( P \cap T = P \). This means that the intersection of the set of all parallelograms and the set of all trapeziums is simply the set of all parallelograms.

### Final Answer:
\( P \cap T = P \)