need help with this problem please 2 Let A B p S where S ENI

need help with this problem please

2. Let A, B p (S) where S ENIsas9) A- 21 and B- 3 Find (a) p (A) (b) (s B)n A 3, Write a counterexample for each property the relation does not possess.

Solution

Set S denotes the set of all natural numbers between 1 and 9.

2 | x denotes the numbers divisible by 2. Set A denotes the numbers divisible by 2.

Set B denotes the numbers divisible by 3.

Part A

(A) would contains the set of numbers divisble by 2 in the range 1 and 9.

Hence (A) = {2,4,6,8}

Part B

B = {3,6,9}

B\' = { 1,2,4,5,7,8,9 }

S - B\' is nothing but B.

B intersection A = {6} which is divisble by both 2 and 3 in the range 1 to 9.