document.write( "Question 1047234: Suppose Set B contains 61 elements and the total number elements in either Set A or Set B is 112. If the Sets A and B have 38 elements in common, how many elements are contained in set A? \n" ); document.write( "
Algebra.Com's Answer #662777 by Theo(13342)![]() ![]() You can put this solution on YOUR website! set B contains 61 elements. \n" ); document.write( "total number of elements in set A or set B is 112. \n" ); document.write( "sets A and B have 38 element in common.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the formula is number of elements in set (A or B) is equal to the numbers of elements in set A plus the number of elements in set B minus the elements that are in both set A and set B.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the formula assumes that the elements in set A include the elements that are also in set B, and it assumes that the elements in set B include the elements that are also in set A.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "because of this, the elements in set A and B are double counted, once as part of set A and again as part of set B.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the subtraction of the number of elements in both set A and B eliminates the double counting.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "112 = 61 + A - 38\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A represents the number of elements in set A\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for A to get A = 112 - 61 + 38 = 89\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "there are 61 elements in set A and 89 elements in set B.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "each set is assumed to contain elements that are in both.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "take out the elements in set A that are also in set B. \n" ); document.write( "take out the elements in set B that are also in set A.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you get the number of elements in set A only are 61 - 38 = 23. \n" ); document.write( "you get the number of elements in set B only are 89 - 38 = 51.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "now count the number of elements that are in both set A and B separately.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you get 23 in A and 51 in B and 38 in both for a total of 112.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |