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)?

A:

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.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: Use the fact that 5x2 – y? = c is a one-parameter family of solutions of the differential equation y…

A:

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

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

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

A:

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

A:

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.

A:

Q: Show dz 4 In= 는I미페 - for a<0. x <

A:

Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

A:

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

A:

Q: for ne J, x is a (1-x)(1+x+x²+.. + x^²) = 1=x^²+₁ variable, prove that

A:

Q: is it proveable with only the theorem given?

A: Is it provable with only the theorem given?The notations and symbols in the given theorem are used…