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1. Let A = {1,2, 3,..., n}
(a) How many relations on A are both symmetric and anti-symmetric?
(b) If R is a relation on A that is anti-symmetric, what is the maximum number of ordered pairs that can be in R?
(c) How many anti-symmetric relations on A have the maximum size that you determined in part (b)?
In a garden, 1/8 of the flowers are tulips. 1/4 of the tulips are red. What fraction of the flowers in the garden are red tulips?
(e) Solve the following system of equations by using Matrix method. 3x + 2y + 2z = 11 x + 4y + 4z = 17 6x + 2y + 6z = 22
howmany numbers made by digit 0,1,2,3,5,7,9 but any digit isnot repeted
In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti
P and Q are the points (12,0) and (0,-5) respectively,find the length of the median through the origin O of the triangle OPQ
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is this free for LIFE that means forever never ever going to pay
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1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0. (a) Prove that R is an equivalence relation on S, an
For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you
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