By K. S. Snell, J. B. Morgan, W. J. Langford and E. A. Maxwell (Auth.)
ISBN-10: 0080107826
ISBN-13: 9780080107820
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Extra info for Elementary Analysis. Volume 1
Sample text
Hence, from (i) and (iii), the number of times when all three coins showed heads together was between 18 and 27, and they showed tails together not more than 25 times. 2 1. The statement P c Q can be written P n Q = P. Write it as an equation in two other ways. 2. When is the statement (A u B) n B' = A true? 3. Prove that (i) (A n B) v (A n B') = A, (ii) A u {Af n B) = A u B. 4. In a class of 33 children, 26 have had mumps and 25 have had chickenpox, what can you say (i) about the number who have had both, (ii) about the number who have had neither?
U) = (a6). u (Distributive). It is now clear that we have an unusual set of operations. Vectors alone, under the operation of addition, form a closed system following the commutative and associative laws, and have a zero and an additive inverse. Vectors under scalar multiplica tion also form a closed system following modified laws of associa tion and distribution, with a scalar zero and a scalar unit. We shall now examine some of these properties when vectors are presented as ordered pairs. OP.
Write down the coordinates of Gi, and of the point which divides AGi in the ratio 3:1. Repeat this process for G2, the centroid of AACD, and BG2. What can be deduced about the lines joining the vertices of ABCD to the centroids of the opposite faces ? 6. P, Q, R, S are the centroids of the faces BCD, ACD, ABD, ABC of the —> —> tetrahedron ABCD. Show that BA = 3Pß, and deduce that ABCD and PQRS are homothetic. What information does this give about AP, BQ, CR, 2)5? Congruences The time shown by a 12-hour clock never exceeds 12 hours, reverting repeatedly to zero and turning on again towards 12.
Elementary Analysis. Volume 1 by K. S. Snell, J. B. Morgan, W. J. Langford and E. A. Maxwell (Auth.)
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