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The Venn diagram for the above facts is given below. Example 16 If in a city 60% of the residents can speak Bengali and 50% can speak Kannada, What percentage of residents can speak both the languages, if 20% residents can not speak any of these two languages? e. e. n(B Ç K) = 60 + 50 – 80 = 30 Therefore 30% of the residents can speak both the languages Bengali and Kannada. Example 17 In a survey about liking for colours, it was found that everyone who was surveyed had a liking for at least one of the three colours namely Red, Green and Blue.

F) 5 + 2 = 7 if 7 - 2 = 5. 6. Write the truth value of each of the following statements. (a) Sun rises in the south. (b) Man is mortal. (c) Delhi is the capital of India. (d) If three sides of a triangle are equal, then it is an equilateral triangle. (e) (11101)2 + (1)2 = (11110)2 (f) (11101)10 + (1)10 = (11110)10 (g) (11111)2 + (1)2 = (100000)2 and (111)2 = (7)10 (h) (270)8 + (5)8 = (184)10 or (11101)2 + (111)2 = (100101)2 (i) 22 = 9 if and only if 2 ¹ 3 (j) (111)2 + (010)2 = (1001)2 if and only if (1001)2 – (010)2 = (111)2.

If in a city 70% of the residents can speak Tamil and 50% can speak Kannada, what percentage of residents can speak both the languages, if 10% residents cannot speak any of these two languages? 18. Let X, Y, Z and T be four sets. Then Prove that (X Ç Z) ´ (Y Ç T) = (X ´ Y) Ç (Z ´ T) 19. Write the following sets as the union of fundamental products. (a) A Ç (B È C) (b) Ac Ç (B È C) (c) A È (B Ç C) (d) A È (B – C). 20. Identify the smallest set X containing the sets. {Book, Pen}; {Pen, Pencil, Box}; {Book, Box, Ball}.

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Aesthetics of Silence by Susan Sontag


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