((X < 5) v (X < 3)) ^ ((X < 2) v (X < 1))

To simplify the expression \(((X < 5) \lor (X < 3)) \land ((X < 2) \lor (X < 1))\), let's break it down step by step.

1. Identify the components:

   • The first part, \((X < 5) \lor (X < 3)\), means that \(X\) is less than either 5 or 3. Since 3 is less than 5, this simplifies to just \(X < 5\) because if \(X < 3\), it is also true that \(X < 5\).

   • The second part, \((X < 2) \lor (X < 1)\), similarly means that \(X\) is less than either 2 or 1. Since 1 is less than 2, this simplifies to just \(X < 2\).

2. Combine the simplified components: Now we can write the whole expression as: \[ (X < 5) \land (X < 2) \] This means \(X\) must satisfy both conditions, effectively \(X < 2\).

3. Conclusion: The simplified expression is: \[ X < 2 \]

So, the final result of the original expression is \(X < 2\).