Question

if A = { x such that x € N , x < =10 } , B ={ 1 , 3 , 5 , 7 } C = { 6 , 8 , 10 } . prove that . A -(B union C ) = ( A-B ) intersection ( A-C)​

Answer 1

Step-by-step explanation:

We take set A values i.e..

A={1,2,3,4,5,6,7,8,9,10} and B={1,3,5,7} and C={6,8,10}

now take LHS

(B union C)={1,3,5,6,7,8,10} [since union means to add both set elements]

A-(B union C)= {2,4,9}---------------equation number 1

[A-(B union C) means to remove common elements in both sets and write remaining A set elements)

and take RHS

A-B ={2,4,6,8,9,10},. A-C={1,2,3,4,5,7,9}

( A-B) intersection (A-C)= { 2,4, 9}---------equation number 2

[intersection means to take common elements in both sets]

equation 1 = equation 2

LHS = RHS