Exercise 1. Let X = {a, b, c, d, e}. Which of the following families is a topology? Why or why not? (1) T= {Ø, {a}, {b}, {a,b}, {d, e}, X}; (2) T= {Ø, {a}, {b}, {a,b}, {d, c}, {a, b, c, d}, X}; (3) T = {0, {a}, {b}, {a,b}, {d, c}, {a,b,c,d}}; (4) T = {0, {a}, {a,b}, {b, c, d, e}, X};

Q: ercise 6.67. Let E be a subset of R having at least two points. Pro- owing are equivalent:

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Q: 1. Let X = {a,b,c} and B={{a,c}.{b,c}}cP(X). Show that B cannot be a base for any topology r on X.

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A: Given that set X={a,b,c}

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Q: 3. Let X = {a,b,c ,d, e}, f ={{a,b}.{b.c}.fc.e}.fe}}cP(X) Find the topology z on X generated by B.

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Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: A = {q, s, u, w, y} B = {q, s, y, z} C= (v, w, x, y, z). List the elements in the set. (Au B)'n C

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