The sets S and E are defined as given below:
`S={(x,y): |x-3|lt1and|y-3|lt1}` and
`E={(x,y):4x^(2)+9y^(2)-32x-54y+109le0}`.
Show that `SsubE`.

Explanation

To show that the set \( S \) is a subset of the set \( E \), we need to analyze both sets based on their definitions.

### Step 1: Define Set \( S \)

The set \( S \) is defined as:
\[ S = \{(x,y) : |x-3| < 1 \text{ and } |y-3| < 1\} \]
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