set of x " Η ②Let x be aset and C-p(x) "The power The collection of all subsets of x is a topology on x called discrete topology >> = {} {A ≤ x /A finite (3) Let x be aset and I be the collection of all subsets of x whose complements are finite together with the empty set then I is a topology on x called cofinite topology 1 or finite complement topology. [U{ACX/A countable} Let x be aset and I be the collection of all subsets of x whose complements are Countable set together with empty set then T is a to topology on x called Countable] topology

Q: What are the right three digits of 3402? Hint. Use Euler's theorem. What is o(1000)?

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Q: 1 Show that u(7) -

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Q: 1+ sin 0 csc0+1 1-sin 0 csc0–1 II

A: We have to prove the identity.

Q: Show that Sn is solvable when n ≤ 4.

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Q: . Prove that an→L = Jan] → |L]. (Make cas

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A: We need to prove the identity  csc2z-cot2z=1

Q: State the Fermet's Last Theorem. Who was French women mathematican who mede significant 19th century…

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Q: Prove that.

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Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: Prave that toc all numbers a and b, if (a,b)=d and az df, b=dq+ then df, 6=dg, then.

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Q: Prove that diyrwl

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Q: is R* is contractible?

A: This is a problem of Topology.

Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: If z1:2., are complex numbers such that =|= =. = |=,| =1, Prove that

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A: Solution: The objective is to prove that the given statement

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A: We find complex number

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Q: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: Which is the most famous theorem of pierre de fermat?

A: To tell which is the most famous theorem of Pierre de fermat

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A: To compute and a and b.

Q: Find gcd(1000, 34) and lcm(1000, 34) and verify that gcd(1000, 34) · lcm(1000, 34) = 1000 · 34

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Q: is it proveable with only the theorem given?

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