Let's break down the given statement and analyze it step by step:

We have:

• $x = 3$
• $b = (2, 5, 4, 8)$

The statement is: $x > 1 \land \exists x (0 \leq x < 4 \land b[x] < 3)$

Step 1: Check if $x > 1$

• $x = 3$, so $x > 1$ is true.

Step 2: Check if $\exists x (0 \leq x < 4 \land b[x] < 3)$

• We need to check if there is an $x$ in the range $[0, 4)$ such that $b[x] < 3$.
  • For $x = 0$, $b[0] = 2$, which is less than 3, so this is true.

Therefore, the second part of the statement is true.

Final Evaluation:

Since both parts of the statement are true, the entire expression is true.

So, the statement is True.

Would you like further details on any part of the explanation? Here are some related questions you can explore:

1. What is the meaning of existential quantification in logic?
2. How do we interpret tuples in logic expressions like $b[x]$?
3. What is the difference between universal and existential quantifiers?
4. Can you prove the statement using different values for $x$ or $b$?
5. How would the result change if $x$ was another value, say 1?

Tip: In logic, the placement of quantifiers ($\exists$, $\forall$) is crucial for understanding how conditions apply to variables.