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Then G N × A× B defined by G = F h is a surjection By part (c) of Proposition 36, the set A×B A×B is countable Corollary 39 The set Q of all rational numbers is countable Proposition 310 Assume that the set I is countable and Ai is countable for every i ∈ I Then S± ² ³ ´ µ ¶ ¸ ¸ ¹ º » ¼ ° µ ½ ± ¶ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ò Ñ Õ Í Ï Î Ü Ý Þ ß à á â Ü ã ä å æ ç èNCERT Solutions Class 11 Maths Relations and Functions – Free PDF Download NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions are solved in detail in the PDF given below All the solutions to the problems in the exercises are created in such a way, that it enables the students to prepare for the first term exam and ace it

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P)∶x i∈Gandx 1x 2 x p=1} a) Show that S has SGSp−1 elements, hence has order divisible by p Proof Since the ptuples are unordered, we can arbitrarily choose the p−1 left coordinates in SGSp−1 number of ways Then, the coordinate x p is given by the inverse of x 1 x 2 x p−1 De ne the relation ∼on S by letting ∼ if is a cyclicX Y Z \ ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z {} ~ p r q x z t s o y ü ý þ ÿ !Definition 15 For p > 0, the function f(x) = px = exlnp is called the exp function with base p Properties d dx px = px lnp ⇒ Z px dx = 1 lnp px C, for p > 0, p 6= 1 Other Bases f(x) = log p x, p > 0 Definition 16 For p > 0, the function f(x) = log p x = lnx lnp is called the log function with base p Properties d dx log p x = 1 xlnp 9

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