State whether each of the following statements are true or false. If the statement is false re-write the given statement correctly: `(i)` If `p={m , n}a n d\ Q={n , m},\ t h e n\ PxxQ={(m , n),\ (n , m)}` `(ii)` If A and B are non empty sets then `AxxB` is a non empty set of ordered pairs `(x , y)` such that `x in B\ a n d\ y in Adot` `(iii)`If `A={1,2},\ B={3,4},\ t h e n\ Axx(Bnnvarphi)=varphidot`

Explanation

Let's analyze each statement one by one and determine whether they are true or false. If false, we will rewrite them correctly.

### Statement (i):
**Given Statement:** If \( P = \{m, n\} \) and \( Q = \{n, m\} \), then \( P \times Q = \{(m, n), (n, m)\} \).

**Solution:**
1. **Understanding Cartesian Product:** The Cartesian product \( P \times Q \) consists of all ordered pairs \( (x, y) \) where \( x \in P \) and \( y \in Q \).
2. **Elements of P and Q:** Here, \( P = \{m, n\} \) and \( Q = \{n, m\} \).
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