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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
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7(y + 3) - 2(x + 2) = 14, 4 (y - 2) + 3(x - 3) = 2 Ans: 7(y + 3) - 2 (x+ 2) = 14 --------- (1) 4(y- 2) + 3(x - 3) = 2 ----------(2) From (1) 7y +21 -
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1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by
how do you solve 45 = n/5 = 5
Decision Theory Decisions There are many types of decision making 1. Decision making under uncertainty It refer to situations where more than one outcome can r
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
y=X^2/3(2X-X^2)
let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?
Testing the hypothesis equality of two variances The test for equality of two population variances is based upon the variances in two independently chosen random samples drawn
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