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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, and describe the distinct equivalence classes of R.
(b) Why is the relation R2 on S given by xR2y iff xy < 0 NOT an equivalence relation?
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2x40 420x4 7x240 84x20 Explain how three expressions are equivalent.
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
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Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.
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