If P is the set of all parallelogrma, 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 of finding the intersection of the set of all parallelograms (P) and the set of all trapeziums (T), we can follow these steps:

### Step 1: Understand the Definitions
- A **parallelogram** is a quadrilateral with both pairs of opposite sides parallel.
- A **trapezium** (or trapezoid in some regions) is a quadrilateral with at least one pair of opposite sides parallel.

### Step 2: Analyze the Relationship Between the Sets
- Since every parallelogram has two pairs of opposite sides that are parallel, it satisfies the condition of having at least one pair of opposite sides parallel, which means every parallelogram is also a trapezium.

### Step 3: Determine the Intersection
- The intersection of two sets, denoted as P ∩ T, consists of all elements that are common to both sets.
- Since all parallelograms are trapeziums, the intersection P ∩ T will include all parallelograms.

### Step 4: Conclusion
- Therefore, the intersection P ∩ T is equal to the set of all parallelograms, which is P itself.

Thus, we can conclude that:
\[ P \cap T = P \]