Question

U = {1,2,3,7,8,9,10,11,12}
P = {1,3,7,10}
then show that (P')' = P

Answer 1

Step-by-step explanation:

Given :-

U = {1,2,3,7,8,9,10,11,12}

P = {1,3,7,10}

To find :-

Show that (P')' = P .

Solution :-

Given that

U = {1,2,3,7,8,9,10,11,12}

P = {1,3,7,10}

We know that

P' = U-P

=> P' = {1,2,3,7,8,9,10,11,12} - {1,3,7,10}

=> P' = {2,8,9,11,12}

and

(P')' = U - P'

=> {1,2,3,7,8,9,10,11,12} - {2,8,9,11,12}

=> { 1,3,7,10}

=> P

Therefore (P')' = P

Hence, Proved.

Answer:-

(P')' = P

Used formulae:-

→ Let U be the universal set and A be a non empty set then A' = U-A.

→ The set of all elements which belongs to only U and does not belongs to A is called A'.