Given sequence is . Now use the ratio test,
Now the limit is .
Thus the series diverges..
If n(A ∪ B) = 97 and n(A) = n(B) = 64, find n(A ∩ B).
If n(U)= 40, n(A)= 19, n(B)=12, and n(A U B)’ =13. Find n(A intersect B).
Suppose that |A| = |B| = |C| = 100, |A n B| = 60, |A n C| = 50, |B n C| = 40, and |A U B U C| = 175. How many elements are in A n B n C?
4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B 1-A and A2 = A. Show that AB-BA-0 4. Let A and B be n x n such that B = 1-A and A2 = A. Show that AB BA = 0 4. Let A and B be n x n such that B...
A and B are n* n matrices. show that (b) Show that if there is a 1 ER such that A - 1I is similar to B - 11, then A is similar to B.
Suppose A and B are disjoint sets with n(A) 17 and n (B) 10 Compute n (A U B)
Prove the following languages are not context-free by using the pumping lemma. {b(n) #6(n + 1) | n є N, n-1} where b(n) is binary representation of n with no leading 0 {b(n) #6(n + 1) | n є N, n-1} where b(n) is binary representation of n with no leading 0
P(A)= .3 P(B)=.4 P(C)=.5 Find P(A n B n C') P(A n B' n C) P(A' n B n C) show all work please Use Venn diagrams mutally independent
lei n be ositive intcger. Find the cardinality of the sci {(A, B) : A, B C [n] and An Bメ0) lei n be ositive intcger. Find the cardinality of the sci {(A, B) : A, B C [n] and An Bメ0)
a. Let B be an n x n Orthogonal matrix, that is B^-1 = B^T, and let A be an n x n skew-symmetric matrix. Simplify A(A^2(BA)^-1)^T b. Let A be a square matrix such that A^3 = 0. A is then called a nilpotent matrix. Define another matrix B by the expression B = I - A; Show that B is invertible and that its inverse is I + A + A^2 c. Let B = (-2,0,0 ; 0,0,0...