Relations and Functions

Relations and Functions

Question

If X and Y are two sets such that (X ∪ Y) has 18 elements, (X ∩ Y) has 5 elements and set Y has 15 elements. How many elements set X have ?

Answer
space space space space space straight n left parenthesis straight X union straight Y right parenthesis space equals space 18
  
space space space space space straight n left parenthesis straight X intersection straight Y right parenthesis space equals space 5
   
      n(Y)    = 15
We have,  space space space space space space space space space space space straight n left parenthesis XUY right parenthesis space equals space straight n left parenthesis straight X right parenthesis space plus space straight n left parenthesis straight Y right parenthesis space minus space straight n left parenthesis straight X intersection straight Y right parenthesis

space space space space space space space space space space rightwards double arrow space space space 18 space equals space straight n left parenthesis straight X right parenthesis space plus space 15 space minus space 5

space space space space space space rightwards double arrow space space space straight n left parenthesis straight X right parenthesis space equals space 18 space minus 15 space plus space 5 space equals space 8
Hence, number of elements in set x = 8

More Chapters from Relations and Functions