5. If {T,} is a family of topologies on X, show that Ta is a topology on X. Is UT, a topology on X? Discuss your answer.

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Q: 6. Let A = {1, 2, 3, 4} R = {(1,2), (1,3), (2,3), (2,4), (3,1)} S= {(2,1), (2,4), (3,2), (3,3),…

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A: Modus ponens says that: ∀x if Px then Qx∃ x Px∴∃ x Qx This argument is valid.

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Q: 8. Solve the following IBVP: U = u + sin(3nr), 00, u(0, t) = u(1, t) = 0, t20, u(r,0) = sin(72),…

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