Answer :

varshamittal029

The cardinality of the set (A − C) n B is 35 .

  • Cardinality of a set is defined as the number of elements in the mathematical set. It can be finite or infinite. For example,  the set A = {1, 2, 3, 4, 5, 6} has cardinality 6. Because the set A has 6 elements. Set cardinality is also known as set size.
  • A real number can be defined as a combination of  rational and irrational numbers. They can be both positive  and negative, denoted by the symbol "R".
  • Natural number all count numbers starting at 1.  N = {1 ,2 , 3 ,4, .....}

We have given three sets A = {x | x ≤ N} where N is a natural number .

Then , set A will get values [tex]A= \{1,2,3,4,5......\}[/tex]

B = {x-5 < x < 105, x ≤ R} where R is a real number whose values is in domain of (- ∞ ,∞)

Then , set B will get values [tex]B=(-5,105)[/tex]

C = {x|x is a rational number, 10 < x < 80} rational number which can expressed in [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex] .

Then , set C will get values [tex]=(10,80][/tex]

According to the question

(A − C) n B [tex]=(\{1,2,3,4,5 ........\}-(10,80] \sqcap (-5,105)[/tex]

                  [tex]=\{1,2,3,4,5,6,7,8,9,10,81,82,83 .......\} \sqcap (-5,105)\\[/tex]

                ={1,2,3,4,5,6,7,8,9,10,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103, 104 ,105}

                   

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