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Suppose A and B be two non-empty sets then every subset of A Χ B describes a relation from A to B and each relation from A to B is subset of AΧB.
Consider R : AΧB and (a, b) € R. then we can declare that a is associated to b by the relation R and write it as
a R b. If (a, b) ¢R, we write it as a b.
Example Let A {1, 2, 3, 4, 5}, B = {1, 3}
We set a relation from A to B as: a R b iff a ≤ b; a € A, b € B. Then
R ={(1, 1), (1, 3), (2, 3), (3, 3)}AΧB
Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0. (a) If (x n ) converges to x, show that (|ax n + b|) converges to |ax + b|. (b) Give
(x+4)(x+6)>0
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(a) Assume that A is a m 1 ×m 2 matrix and B is a m 2 ×m 3 matrix. How many multiplications are required to calculate the matrix product AB? (b) Given that A 1 is a 20 × 50 m
what''s it?
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