The image contains a set of mathematical problems from Section B of an exam or worksheet. I will provide a step-by-step solution to any question you choose. Let me know which problem you'd like me to solve or explain in detail. Here is a quick summary of the questions:

Section B (Answer any SIX)

9. Verify $A \times (B \cup C) = (A \times B) \cup (A \times C)$ for given sets $A = \{1, 2, 3, 4\}, B = \{3, 4, 5\}, C = \{3, 5, 6, 7\}$.

10. Prove $f(x) = 2x + 3$ is one-one and onto, and find the inverse of $f$.

11. Show that $\sim(p \to q) \leftrightarrow (p \land \sim q)$ is a tautology.

12. Solve $\binom{2n}{3} : \binom{n}{2} = 44 : 3$ and find $n$.

13. Using the Cayley-Hamilton theorem, find $A^{-1}$ for matrix $A = \begin{bmatrix} 3 & -1 \\ 4 & 5 \end{bmatrix}$.

14. Solve the system of linear equations using Cramer’s rule: $2x + 3y + z = 9, \quad 4x + y = 7, \quad x - 3y - 7z = 6.$

15. Define isomorphism of graphs. Verify whether the two graphs shown are isomorphic or not.

16. Define a Hamiltonian circuit. Check whether the given graph contains a Hamiltonian circuit and justify your answer.

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