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Write true (T) or false (F) for the following statements:(i) If a divides b, then a3 divides b3.(ii) If a2 ends in 9, then a3 ends in 7.(iii) If a2 ends in an even number of zeros, then a3 ends in 25.(iv) If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros |
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Answer» (i) If a and b are integers such that a2 > b2, then a3 > b3. In case of negative integers, (-5)2 > (-4)2 = 25 > 16 But, (-5)3 > (-4)3 = -125 > -64 is not true. Statement is False. (ii) If a divides b, then a3 divides b3. If a divides b b/a = k, so b=ak b3/a3 = (ak)3/a3 = a3k3/a3 = k3 For each value of b and a its true. Statement is True. (iii) If a2 ends in 9, then a3 ends in 7. Let a = 7 72 = 49 and 73 = 343 Statement is True. (iv) If a2 ends in an even number of zeros, then a3 ends in 25. Since, when a = 20 a2 = 202 = 400 and a3 = 8000 (a3 doesn’t end with 25) Statement is False. (v) If a2 ends in an even number of zeros, then a3 ends in an odd number of zeros. Since, when a = 100 a2 = 1002 = 10000 and a3 = 1003 = 1000000 (a3 doesn’t end with odd number of zeros) Statement is False. |
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